Peer to peer (P2P) networks allow individuals to connect their PCs directly to other people's PCs, in order to share files. In order to use one of these networks, you require some appropriate software, known as a 'client'.
The most well-known P2P client is Limewire, which connects PCs together by using a network called Gnutella. The majority of users use the client, and the network, to (illegally) share copyright music and video files.
However, Gnutella is not the only P2P network. Two of the others are called eDonkey and Kad. eMule is a client which can connect into either of these networks.
So, eMule is similar to Limewire but uses different networks.
Chris