Perlin noise
Also said as Gradient noise, Fractal noise, Octaves, fBm
Random numbers that change smoothly, made by Ken Perlin. Add several layers, called octaves, each twice as fine and half as strong, and you get something that looks like hills and rock.
Plain randomness looks like television static. Smooth noise has the large shapes and small details natural things have, and it needs no storage: any point can be worked out on demand.
Say it
“Use Perlin noise for the terrain height, 5 octaves at a gain of 0.5. Add a second, slower layer for biomes, so forests and deserts come in large connected patches.”
Where you’ve seen it
Minecraft's terrain uses it: Notch has described it as interpolated 3D Perlin noise offset along the height axis. Perlin himself won a 1997 Academy technical award for the technique.
Not to be confused with white noise
In white noise each value ignores its neighbours, so it looks like static. In Perlin noise neighbours are close in value, so it looks like terrain.