Hm... say there is "server1.undernet.org" and "server2.undernet.org"
this servers toogerther are undernet network.
Note: When there is a split it means that something went wrong in connection of server1.* and server2.* so the users that are in server1 cannot see users in server2.* and the same for users in server2.*
At the moment are toogether
at 9:00 in the morning there was someone in the server2.* with nickname FallGuy (for example

). Users from server1.* could see him and talk to him because the servers were toogether.
at 10:00 in the morning a net split occured and server2.* splited with server1.* now users in server1.* saw user FallGuy quitting with reason (Net*Split) but actualy he didn't quit he is just in server2.* and can no longer see him users from server1.*
at 11:00 you join server1.* with nickname FallGuy. Everything ok because there is no nickname FallGuy in the network (at the moment the network is only server1.*)
at 12:00 server2.* comes back with server1.* but something is wrong here. There are 2 users with nickname FallGuy. So the user who came last (and in this case its you) gets quit with the message you saw and the other continues regulary in UnderNet.
I hope if you didn't understand with andrews' desc you understand better with this one
