Hello DC,
As a one non-native speaker to another (to you) I will try to explain to you how I grasped the difference between two tenses, which might be useful to you in this case. Teachers, feel free to rectify my explanation if I am mistaken.
So, in first case you mentioned particular period of time when some event happened- last meeting - which means it already happened then and event is finished. That requires past simple.
For example :" I DID my homework yesterday" (I am telling you now that I completed my duties yesterday and it's closed chapter now).
On the contrary, your second case indicates that you have done something before in non specific period of time which might be still lasting in the present.
For the sake of clarity: "I have met him several times" ( I am telling you now that I had several meetings with him, but who knows if we will ever meet again, maybe we will, maybe not. I didnt mention particular time framework). In the nutshell- usually when you use some particular time references for the event that happened in the past, like "yesterday", "last year", "last week"....- past simple tense should follow!
I hope that my explanation helps, because I know how difficult could be to decipher some things as a non native.
Once again, for the sake of punctuality and proper learning - I am not a teacher and please feel free to rectify, correct or delete my post if you think it's confusing or terribly wrong.
