How can an undergraduate student conducting mathematical research with a professor expect to contribute?
It's very reasonable to wonder how you, an absolute novice, could "help" experienced experts. Some people are fond of claiming that somehow "just trying hard" or "being smart" can make this possible in some way, but those are needless (and doubtful) claims that miss the mark about what the real question could be.

That is, many or most faculty are happy to mentor beginners and introduce them to the subject(s) the faculty know and like. It need not be the case that they "need help", and, if they did, sure, recruiting novices is not the best gamble. But that's not the point! The point is that experts may enjoy (and find stimulating) introducing beginners to their subject. So you help them by allowing them to do so.

It's not at all surprising that you have trouble reading their recent papers, and, again, that's essentially irrelevant. (The internet mythology about young people becoming world experts in a few weeks or months is invidious... In particular, no, you should not expect to "read those papers and then go talk to them about them.", contrary to much advice given on-line.)

An astute expert can find interesting "starter" projects for novices. It may happen that such a project produces something interesting to the expert. Or, it may be that the expert can so well foresee the outcome that the element of surprise evaporates. But that doesn't matter. Little kids don't have to immediately play sports (or whatever) with world-class professionals. But they can be coached by such professionals, if both parties are interested. I do think that's the correct analogy, though many other people on these sites are adamant otherwise.