Mitte was the center of east Berlin and you can easily find it as the famous TV tower is right in the middle of Alexanderplatz.
It's a huge area that is often misunderstood. For some, it's where all the cool shops are, for others, that's the place to go for art galleries. Mitte has ugly but somehow romantic Soviet block houses, empty houses, huge abandoned pieces of land, super-expensive streets, and dirty corners. It's a huge area that seems to encompass a few cities in one.
You might hear "mitte fashion", which became an almost derogatory term for describing the local crowd, but one thing is for sure: if you want something a bit more fancy in this city that is not (too) tacky at the same time, Mitte is the place to go.
The best way to start exploring it is to walk from Alexanderplatz to Hackerschermarkt, then walk towards Torstrasse, have a coffee in a few cafes along the way, and then if you've got time walk towards Brunnenstrasse to experience the real local feel of the area.