aMule is basically the successor to eMule, which is the successor to the freeware eDonkey2000, which by the name you can tell is quite old. Anyways, the main point of eD2K is that it relies on a server that anyone can host using a freeware app called eserver, to which clients connect.
So instead of torrents, which are shared between each peer without a centralizing server, eD2K needs thoose servers.