An Era is a period of time on MCPE in which entails the timeline of a map's run on the server from when it is opened to the public to when it is replaced with a new map. Eras do not have a timespan that is necessarily set in stone, with most Eras so far lasting around 7-9 months before being replaced with a new map in order to generate new interest in the server amongst players and staff alike.
So far, MinecraftPlanetEarth has had 9 complete Eras, and is currently on Era 10.