This depends on what you are referring to - is it something current or in the past? I don't understand is present tense. You could say, "I don't understand what you are [currently] saying" I didn't understand is past tense. You could say, "I didn't understand what you said five minutes ago"

I don't understand = now I didn't understand = past I don't understand your question. I didn't understand your question (before) but someone helped me (to understand), so I do understand (it) now.