Verstaan is when you can hear what someone is saying: ik kan hem verstaan. (i can understand him/ i hear him)
Begrijpen is when you understand what someone is saying: ik begrijp what je bedoelt. (i understand what you mean)
So in the case of: ik versta je, maar ik begrijp niet wat je bedoelt. You can hear what he is saying, but you do not understand what he means by it.