The village of Köpenick was incorporated into the greater berlin area in 1920 but the former town actually has a history which is older than any other part of the greater Berlin area – including the town of Berlin which it has become a part of.
The city has a nice center which is fairly charming and worth a little day trip out from the central part of Berlin. The borough is a lot more quiet than the central part of Berlin so it is a good place to go if the hustle and bustle of Berlin becomes too much and you want to go and relax for a bit. There is a lake in the area as well so it is a pretty place.
The easy way to get to the old town is to catch the S-bahn to the Köpenick stop and then catch a tram to get to the old center of Köpenick – it is possible to walk as well in around 20 minutes I guess from the S-bahn stop.