For humans, noise is simply a perception of subjects being distorted. Noise is often associated with sound however it is possible to perceive noise for visuals. In computer programming noise is used to mimic real life variance. By generating organised pseudo random numbers it is possible to realistically draw anything from wood, clouds or any other naturalistic texture. Ken Perlin invented one of these methods for generating noise in computer science way back in 1983. Like all good programming ideas (think Boids) this is still very popular today and used in games and apps alike.
This playground example is an attempt to generate a 3D cube made up by smaller 3D cubes and have each segment scale based on a 2D generated Perlin Noise texture. The texture is used as a table with rows and columns to lookup scalar values. The "smoothness" of the noise is mostly down to the Perlin noise algorithm. By seeding different values for the algorithm we can achieve slower transitions or more abrupt changes in randomness.
Note: The 2D renders below is not what Perlin noise look like. I've leave that for you to Google. But instead these are 2D drawings using Perlin noise.