What is a DVD Region?
To try to prevent piracy (and maximise revenue), the DVD manufacturers divided the worlds DVD market into different regional areas. This prevents DVD’s from one region working on a player from another region.
A map of the worlds DVD regions
How can I play a disc from another region?
There are really two ways for you to play a disc from another region. You could import a player from the region you require or you can make your DVD player region free. Obviously the former option is not very practical if you want to play disks from more than one region. As for a region free player, there are several ways that this can be done. You can buy a player that has already been “chipped” for region free from a mail order retailer. You can sometimes buy a chip to fit into your player. You can also “hack” certain players to be region free through its (or another) remote control. All of these options depend on the model of player that you choose to purchase. A search on Google for your make and model of player and "Region Free" should produce relevent links.
Any other issues?
The only other thing you need to worry about when playing disks from other regions is the fact that they are recorded in the local broadcast format. For example if you buy a US disk it will be recorder in NTSC, which runs at a different frequency to PAL (UK). You need to ensure that your television will support this format.