In my experience graduate students are not trained, or given much experience, in explaining and motivating what they do to other humanists, and each discipline can survive without much contact with other disciplines, so we can pretty much go our own way. For a discipline that places so much value on rigour, explicitness, and clarity, it is striking that most of us cannot articulate to nonphilosophers (or even to our students) definitive criteria for “philosophical interestingness”, which is one of the key values in the discipline.
I think that's pretty obviously because there is no such thing as a definitive criterion for philosophical interestingness, there never was even a plausible candidate for it that would have had widespread acceptance, and of it is one of the key values in the discipline (the words are certainly used a lot) it is a bad sign for the discipline. Philosophers use 'interesting' like they use 'clarity': in particular cases its meaning may be fleshed out by its context, but there is no generally applicable concept used when it is talked about in general.
And surely we can see why? 'Interesting' makes implicit appeal to means-end reasoning; to say that something is interesting means saying that it has (probable) importance, even if only indirect, for something. But philosophy as a field is so vast in scope that pretty much everything in it is interesting for something. Thus talking about whether a philosophical problem is interesting is really just throwing the whole question back one step; interesting for what? But if we really accept that things are interesting for reasons that relate them in important ways to other things, then it seems clear enough that most of the usage of the term by academic philosophers is uncritical and poorly thought-out in the first place. We can't explain interestingness because there is nothing sufficiently thought-out enough that it can be the sort of thing that can be explained. We have our interests, and things that fit those we regard as interesting; but 'philosophically interesting' is a phrase used with very little critical thought.
Incidentally, I have beaten this drum before, but I think it is false that we put much emphasis on rigor, explicitness, and clarity; or rather, while we put a lot of emphasis on the words, it seems clear to me that we do not use them in any consistent way or with any general meaning. I've argued this before on the topic of clarity (and here), but I think it is true of rigor and explicitness, as well. Perhaps it's working in an area of philosophy that depends very heavily on evidence that leads me to think this, but I think philosophers tend to be extraordinarily sloppy, not rigorous, when it comes to using evidence; and I likewise think that philosophers very often tend to leave essential assumptions unstated -- for that matter, it is in some cases difficult to get people to recognize the essential assumptions of their own arguments unless you sit down and walk them through proof that they are assuming it, point by point. (Granted, these things are difficult for everyone; but lapses aren't exactly uncommon.) Philosophy as currently practiced uses these words primarily for rhetorical purposes; while they sometimes have solid meaning in particular cases, they don't with any reliability identify anything objective or definite, nor even anything accepted by consensus, but are used to try to persuade. In her memoirs Mary Midgley sums up the problem very well:
Philosophers are always complaining that other people's remarks are not clear when what they mean is that they are unwelcome. So they often cultivate the art of not understanding things -- something which British analytic philosophers are particularly good at.
There are exceptions, of course. But they are, in fact, exceptions.