Minecraft world seeds are generated by entering a string of characters, which can be numbers or letters, into the "World seed" box within the Minecraft menu. As few as one character can be used, and each number will generate a unique world. Text strings are converted by the game to numbers.
The in-game algorithm allows generation of the same world every time, if the same value is input into the seed generator. However, when the algorithm is updated and changed, it no longer generates the same world it did in the past. In other words, seeds that worked for older versions of Minecraft may not work for newer versions. Because the world is only generated up to 10 chunks away from where a player has been, chunks further away than this will be generated according to the new algorithm. This creates sudden terrain changes and cliffs if the algorithm changed dramatically, and more minor terrain inconsistencies if the change was less drastic. These variations can create buildings with missing parts, and can even result in easy access to treasure rooms in Ocean Monuments. Also, it is important to keep in mind that seeds for one version of Minecraft, such as Pocket Edition, may not have the desired result in another version, such as Java Edition. In addition to this, one can select from a variety of preset seeds from the World Creation menu of Minecraft (not Java).
To find the seed of the current world, use the command /seed on PC, or view the world seed in the "World Options" menu.
There are many possible Minecraft world seeds, although only a few will generate unique, interesting terrains and structures.
A list of blog posts that provide examples of world seeds, can be found here.