Between August 13th 1961 and November 9th 1989, Berlin was divided by a physical barrier, which came to be known in most of the world as the Berlin Wall (its official name in East Germany was the 'anti-fascist protection barrier').
As you'll see from the map below, the wall completely surrounded West Berlin, which was like a western island in East German territory. West Berlin was, however, not technically part of West Germany, as it remained under the control of American, British and French forces.
The map shows the side of border that faced West Berlin. Over the course of its existence, the border defences became more sophisticated and the exclusion zone on the East German side got larger; the eastern extent of these exclusion zones isn't currently marked, though it's sometimes possible to spot it on the satellite photos if you're zoomed in close enough.
The pins link to articles about various places which are related to the wall - some have pictures of those places from when the wall was there, others show you what you can see now.