Could you tell me the difference between "3 minutes later" and "in three minutes"?

Question

Answer

a. Three minutes later means "after that time".

For example:
Ann:  Ben, why didn't you do what I said to you:
Ben: I forgot.

(Three minutes later Ben heard some cracks in the kitchen)

Ben: Ah... I am sorry Anna, I am doing it now for you.

b. In three minutes means "around that time not more than that."

For Example:

Clark  :   In three minutes, I want my room clean. No more excuses. I have a very 
               important meeting with my clients. If you mess it, I will fire you!
Janitor:  Copy that, Boss!

Answer

"3 minutes later" is used in the past tense. 
E.g. Yesterday I got out of bed, then three minutes later I made a cup of tea.

It can also be used comparatively
E.g. He got to work three minutes later that usual.

This also works in other tenses
E.g. I have an appointment on Monday so I'll be three minutes later than usual.

"In three minutes" refers to the general amount of time to do something. 
E.g. I can ride my bike to the end of the street in three minutes.

Or it can also refer to when you are going to do something in the future. 
E.g. Can you get the mail? Yes, I'll do it in three minutes.

Hope this helps!