Perlin noise is one of the more important noise basis functions. Ken Perlin got an Academy Award for inventing it, which hints at the impact it has had, both on computer graphics and the world in general.

Unlike the randomness of value noise, Perlin noise is coherent: the value of one point is similar to the value of nearby points. This makes it smoother and gives it larger patterns, which is key in generating interesting results in all kinds of procedural outputs.

Here’s a talk by Ken Perlin himself, all about the noise:
http://www.noisemachine.com/talk1/

Here’s a look under the hood, showing how Perlin noise works:
http://freespace.virgin.net/hugo.elias/models/m_perlin.htm