It helps to go back to the beginning. Intention is, in its origin, an archery term; the word 'tension' goes back to the same root, tendere, which means to stretch, and thus intendere has the implication of stretching the bow so as to direct the arrow somewhere. Because of this the word became a metaphor for attention (also from the same root, and suggesting the idea of stretching your mind toward something); when people told the legend of St. John the Evangelist and the bow, it was more than just a loose metaphor to make a moral point. It was a very clever bit of play on words: the words used to talk about archery and to talk about attention were often the same words. Intention also conveyed, more generally, the notion of aiming at something (which is why you stretch the bow, of course).
Because of this, in medieval philosophy and theology, intentio indicates some kind of aiming. On a broadly Aristotelian view, every example of cause and effect consists of the cause having an intentio for its effect: intentio in this sense is a disposition or orientation to an end, and is the prerequisite for anything acting in this way rather than that or for having this effect rather than that. This is what is going on in the most famous example of a philosophical argument building on the notion of intentio, Aquinas's Fifth Way:
The fifth way is taken from the governance of things. We see that things lacking in cognition, such as natural bodies, operate according to an end, which is clear from their acting always or frequently in the same way so as to result in what is best. Thus it is obvious that they attain to the end not by chance [a casu] but by disposition [ex intentione]. But whatever does not have cognition does not tend to the end unless directed by something cognizant and intelligent, as the arrow by the archer. Thus there is something intelligent by which all natural things are ordered to the end, and this we call God.
In the Fifth Way, intentio doesn't imply that the thing that has it is intelligent, although, of course, the argument holds that there is a connection between intentio and intelligence. But what about human beings? We, too, act and have effects, and since we aren't eternally active, we too have to be given an intention to an end. In our case, we are ordered to universal good, and ultimately that means God. But there are many ways to universal good, so unlike natural things, our will does not have an intention that forces it to follow one and only one path. You might saw that we are arrows that can constantly re-think our way to our target. This is what having free will is. But note that while our choices are our own contribution to our flight to the target, we still do have a target, and all our choices are part of our intention to that end -- they are subordinate parts, and distinguishable from the intention itself, which they presuppose, but they are still part of our intention, in much the way that taking the Interstate rather than the state highway might be distinguishable from but still part of your journey to San Antonio. This is the older, and Thomistic sense (of course, Aquinas is not the only one who uses it, but it is in great measure to Aquinas that the term is still occasionally used this way); it is not so common as it once was, but one still often finds people using it. In this sense, intention includes everything that is essential to your acting the way you do. Analyzing this at a deeper level was one of Aquinas's great achievements: the Treatise on Human Acts is some of the most brilliant work of a man known for brilliant work, and once you start getting an idea of how it all fits together it can be seen to be a stunningly beautiful bit of philosophical work.
However, we can approach things somewhat differently, and Aquinas provides a good jumping-off point for talking about this, too. In talking about goodness and evil with regard to human acts, he notes that there are four different ways you can look at the same action:
Accordingly a fourfold goodness may be considered in a human action. First, that which, as an action, it derives from its genus; because as much as it has of action and being so much has it of goodness, as stated above (Article 1). Secondly, it has goodness according to its species; which is derived from its suitable object. Thirdly, it has goodness from its circumstances, in respect, as it were, of its accidents. Fourthly, it has goodness from its end, to which it is compared as to the cause of its goodness.
So this is an analysis of the action itself. Every action is a kind of action, and thus can be analyzed in terms of genus and species. And the genus, of course, is human action generally (which, of course, presupposed our intention to universal good). The species is determined by what Aquinas calls the 'object'; the object gives form to the action -- it is what makes the action what it is, or is what the action is about. For instance, the object of one's act might be something like to protect my property or to steal John's sheep. As we might put it, the object is what you're trying to do or trying to accomplish.
However, this thing that you're trying to accomplish could be done for many different reasons. For instance, I could be stealing John's sheep because I want to add it to my flock, or to sell it for money, or because I want to hurt John. These have to do with the effects I want to bring about by stealing John's sheep; it's these reasons that lead me to steal John's sheep at all, and this is what Aquinas calls the ends of the action (an action can have many ends, because there can be many reasons for it). It is important to keep in mind that in this context we are talking about the ends of the action itself. There are always other ends involved besides the ends of the action itself; for instance, the only reason the action is possible at all is that the will has an end, universal good, in everything it does. This end is presupposed by the action, but when we talk about the ends of the action, we mean those ends that determine why this particular thing was done rather than anything else. Further, the object of the action is itself a kind of end (which is why we can aim ourselves toward it, e.g., why I can deliberately steal John's sheep), it's just not the end of the action itself (stealing John's sheep is not the reason for stealing John's sheep).
In much modern theology, this scheme is what people primarily use. Since moral theology is always talking about human acts (or things closely related to it), it can take the genus of the action for granted. The determination of the specific kind of action by the object plays a big role in discussion. And when people talk about the ends of the action, it has become common to talk about the intention. It's important to keep in mind that this is the intention of the action itself to its ends, and thus intention in this sense always deals with things other than the action itself. My action is an act of stealing because of its object (taking John's sheep without permission) but I do this because I want to get certain effects out of it (pleasure, money, nice sheep), and intention in this sense deals only with those effects. This sense of the term, if we want a crude and rough comparison to the previous sense of the term, breaks up the previous sense of 'intention' into two parts: the choosing of the object and the intending of the end. (This can be important in discussions of double effect, because the principle can be formulated, and often has been formulated, using either way, and people sometimes shift senses in the middle of their discussion.)
It is this second sense of intention that is found in CCC 1750:
The morality of human acts depends on:
- the object chosen;
- the end in view or the intention;
- the circumstances of the action.
The object, the intention, and the circumstances make up the "sources," or constitutive elements, of the morality of human acts.
In part because of the Catechism, in part because of other documents (like Veritatis Splendor), this is the dominant way of using the term in Catholic moral theology today, although due to the importance of Aquinas, the other way can also be found.
Both of these senses differ somewhat from our ordinary English word 'intention' or 'intent', by which we I think we usually mean less than the first sense and more than the second. Also, I think the conversational sense allows for more self-deception to enter into what we are calling intention than the theological terms: in the theological senses it doesn't matter what you call your action or how you justify it, what matters is what you actually are doing. I can pretend to myself all I please that I am just engaging in economic redistribution; what matters is what I am actually deliberately doing, in this case taking John's sheep without proper permission (which is my object whether I choose to use these particular words to describe it or not) out of malice, or greed, or what have you (which establish my ends as bad even if I use pretty words to justify them to myself). That is, the theological terms are objectivist: they presuppose that you are actually doing something intelligible that can be described in objective terms, and that this is independent of what you might want to pretend you are doing (what ultimately matters is not how you would describe it, although if you are sincere that can influence our evaluation of guilt and innocence a little bit, but how a genuinely virtuous person would describe it); but the conversational use of the term seems to be subjectivist: it's as much about how the action strikes you as about what it is, as much about what you want to believe it is as what a good judge (the virtuous person) would believe it to be.
There are probably other senses floating around, but these three are the ones that come up most in Catholic discussions of ethics, and that most need to be kept distinct in such discussions.