This only applies if you have a v1.xx character. Because of the new datacenter, not all servers will be located in Japan anymore. The servers designated European/North American are now located in North America (most sources point to the new SE datacentre in Montreal, Quebec, Canada). The old servers are being kept but some of them now are being shifted to the North American/European datacenter to reduce lag and such. If you do nothing, your character will stay on the same server it was before ARR. However, if you were on say Aegis but live in North America, you might want to transfer servers because Aegis is remaining at the Japanese datacenter. Or if you wanted to transfer to a server where all your friends or fellow forum memebers go to, say Sargatanas. However, if you do not have a character from v1.xx, none of this is really a worry for you. If you do have a character from v1.xx and do not care what server you are on, then do not worry about it.

As for playing cross-server, this does not occur in the normal game. The only time you can play cross-server is through Duty Finder in Instanced Dungeons/Raids where you are puts into a party with random people from other servers. Outside of that, there is no cross-server playing. Server=World.