An emonBase is a web-connected base-station that receives energy monitoring data from the emonTx and posts to a remote or local server for web-based logging and visualization. This server could be an installation of emoncms or a service like Cosm.
Note on basestation choice: The raspberry pi is not yet the easiest or the most tried and tested base station to use, but it looks like it has the best future development potential. The basestation that has been in use for longest is the NanodeRF which is an Arduino based board the OpenKontrolGateway is also very similar. The NanodeRF will continue to be supported with all firmware and documentation here as usual.