I have dwelt so much on the difficulties which at present obstruct any real knowledge by men of the true nature of women, because in this as in so many other things "opinio copiae inter maximas causas inopiae est"; and there is little chance of reasonable thinking on the matter while people flatter themselves that they perfectly understand a subject of which most men know absolutely nothing, and of which it is at present impossible that any man, or all men taken together, should have knowledge which can qualify them to lay down the law to women as to what is, or is not, their vocation. Happily, no such knowledge is necessary for any practical purpose connected with the position of women is relation to society and life. For, according to all the principles involved in modern society, the question rests with women themselves — to be decided by their own experience, and by the use of their own faculties. There are no means of finding what either one person or many can do, but by trying — and no means by which anyone else can discover for them what it is for their happiness to do or leave undone.
Opinio copiae inter maximas causas inopiae est means 'One of the biggest reasons for being impoverished is thinking you have a lot' (literally, 'belief in abundance is among the greatest causes for scarcity', or 'the idea that one is wealthy is one of the major causes of poverty'). It is a quotation of Francis Bacon, in particular from the preface of the Instauratio Magna; Bacon is talking about knowledge, which is why it comes up here; what Mill says immediately after this is entirely in line with the meaning of the saying. It's worth quoting in context, since Mill is likely assuming that the whole passage would be called to mind by his quotation of the key part:
It seems to me that men do not rightly understand either their store or their strength, but overrate the one and underrate the other. Hence it follows that either from an extravagant estimate of the value of the arts which they possess they seek no further, or else from too mean an estimate of their own powers they spend their strength in small matters and never put it fairly to the trial in those which go to the main. These are as the pillars of fate set in the path of knowledge, for men have neither desire nor hope to encourage them to penetrate further. And since opinion of store is one of the chief causes of want, and satisfaction with the present induces neglect of provision for the future, it becomes a thing not only useful, but absolutely necessary, that the excess of honor and admiration with which our existing stock of inventions is regarded be in the very entrance and threshold of the work, and that frankly and without circumlocution stripped off, and men be duly warned not to exaggerate or make too much of them.
Bacon is concerned with arguing for the importance of doing more along the line of what we call scientific inquiry; this, of course, is not the kind of argument Mill is making. But Mill would see less of a division between what we call scientific matters and political or ethical matters than most people would today; political progress would not be sharply divided by him from scientific progress. Thus it's probably not just incidental that he is quoting philosophy of science in a discussion of government. And the basic line of thought has parallel -- before you could have reasonable thought, men would have to recognize that they really know nothing, and therefore need to learn. But in the political context there is an option that does not exist in the context Bacon is discussing: it is not actually necessary for men to learn all they need to know in order to lay down the law for how women should be women -- they can let the experts decide, namely, the women themselves.
David J. Riesbeck has a very nice little paper on the fact that the Latin quotation has often been mistranslated in notes to editions of The Subjection of Women, and why that matters for interpretation of Mill's argument.