Don't and
mean are present, while
didn't and
meant are past.
For example, if you're talking to someone now, and you have no idea about your interlocutor's words, you can say:
I don't understand what you mean.If the talk happened yesterday, you say:
(Yesterday) I didn't understand what you meant.I don't understand what you meant is also okay and can be used in both the situations described above. In this case, you imply that you still have no idea what your interlocutor meant (some mins ago, yesterday, a week ago, etc).