By "understanding" a piece of mathematics, do you mean:
- anticipating consequences of definitions and theorems?
- being able to determine the truth/falsehood of 'natural-sounding' propositions?
- being able to recognize when a result applies to a given problem?
- being able to apply results to practical problems?
If you said 'yes' to one or more of the above, then your interpretation of the activity of "understanding mathematics" --- and yes, it is an activity --- has a lot in common with, and may in fact be identical to, the enterprise of mathematical research. That is: mathematical research is no more or less than the attempt to better 'understand' our own mathematical ideas, and how they may be fruitfully applied: both to others of our mathematical ideas, and to more "empirically-inclined" situations.
Furthermore, Turing and Gödel demonstrated that this endeavor is sufficently complicated that it cannot be grasped by any algorithmic approach (at least as we currently understand the concept of an 'algorithm'), and the independence of various 'interesting' propositions from our favourite axiom-systems entail that it is open-ended, i.e. it requires creativity and aesthetic taste on our part as to what mathematical ideas are interesting.
Understanding mathematics is the limit of an unbounded process; it doesn't 'happen', and it cannot 'happen'. The best you can do is to simply engage in the activity.
