World generation seeds were added to Minecraft on February 23rd as part of the Beta 1.3 update. A seed is a string of characters used to provide a starting point for the terrain generation algorithm when creating a new world.
Using the same seed to generate two separate worlds will generate the same terrain consistently even on different computers. This means that seeds can be shared between players to generate the same world between them. However, the player's initial spawn point will be random.
To use a seed you have seen on this website click 'More World Options' when creating a new world then paste the seed into the box as shown below:
If you do not enter anything a random seed will be generated.
In Minecraft it is possible to view the seed of a world by pressing F3: