Aside from the learning the theory a lot of being good at math(s) is pattern matching type stuff and the intuition that goes with it. I suppose this is what the author is getting at, practice, practice....
"Young man, in mathematics you don't understand things. You just get used to them." - Jon von Neuman
It's reassuring precisely because it acknowledges that conundrum -- fundamental understanding often comes after a tough, rote (and uncertain) 'getting used to it.' -- so "stick with it," as it were.
I agree with that, because thats what it takes to internalize something, however the quote says understanding never comes. What I wanted to opine on is the idea that you shouldn't be satisfied with not understanding something just because someone tells you so.
You might be taking the quote too literally. I think what von Neumann was getting at is that the abstract world of mathematics is essentially artificial and alien to our natural sensibilities and that if you expect to 'understand' something to its very core you may be misguided. The deeper you go the more counter intuitive things can get.
It reassures me because it feels at times that the people around me who are so 'great' at mathematics are born naturals and that I may as well give up. For me is a great 'leveller' to hear that even the greatest minds struggle with these things, albeit to differing degrees.
"Young man, in mathematics you don't understand things. You just get used to them." - Jon von Neuman
One of the most reassuring quotes I know!