What is the difference in meaning between the aorist and perfect tense?

There is a subtle difference in meaning between these two tenses, which both refer to an action in the past. The aorist tense simply refers to a single, completed (not ongoing) action in the past, i.e. I X-ed, I did X. The perfect tenses refers to the present state which results from an action in the past which can be completed or ongoing, i.e. I have X-ed, I have been X-ing.
This can be clarified with an example. An example of an aorist tense verb would be "he broke a window", which simply refers to a completed action of breaking in the past. "he has broken the window" refers to a similar past action, but focuses on the current state resulting from it, implying the window is currently in a state of having been broken.