What are seeds?

Whenever the game generate a new world, its calls upon an algorithm. This algorithm will output a pseudo-random value that is then used to determine what a world will look like. However, the algorithm will always end up with the same value if the starting point (seed) that the algorithm uses is the same number.  This is why seeds exist to easily generate entirely different worlds from a single value.

Whenever the world generation algorithm is updated, the same seed will no longer generate the same terrain. This is why in some different versions of the game, the same seed will not give the same world.

A world's seed is set when that world is created. By default, it is decided automatically (if so, the game uses the system time as the seed), but it can also be set manually. Set and reuse a seed to replay that world, or use a known seed to play the same world as another player. Either a number or a word/phrase can be used, including negatives.

If the seed or generator changes in saved world, new chunks will be based on the new seed, and will not match those from the old seed (this phenomenon was widely observed with the Adventure Update). Deleted chunks can regenerate if the seed and generator remains the same, but will change if either the seed or generator changes.

It is important to note that since seeds are simply random values read into algorithm and not actually names of different worlds, using a certain seed will not necessarily result in a world with any relevance to the value seed. For instance, using a biome name as your seed will not necessarily result in the creation of a world with primarily that biome.

Credits to Minecraft wiki.