Seeds in Minecraft are called World Generation Seeds. Minecraft Seeds became a feature when the update for Minecraft 1.3 came out on February 23rd, 2011. Basically a seed is a word or a string that gives the terrain builder algorithm of Minecraft a starting point.
What this means is that the world that is generated on your computer with a seed can be generated on another computer if you give that person the seed you used. It is basically the less detailed version of maps. Maps are pretty much saves that are entire worlds with structures that users have built. Seeds are the world as far as where blocks are and what kind of blocks are there. The only thing that will be different with seeds is that the spawn point will be random.
To use a seed you found at Minecraft-Seeds.org simply go to create a world and enter the seed you found in the seed field.
If you do not enter a seed at this point a random one will be generated for you.