I have been reading about Perlin noise and stuff like that. My question is, what has noise got to do with anything? ???
If you don’t know, then read more.
In a visual sense, noise is an element of chaos: pure noise is what you used to see on ancient televisions when there was no signal:
Perlin noise is also chaotic, but less so than pure noise. Haha, I guess it’s hard to explain for me. Anyone else got an idea?
Noise was originally a term from sound processing and “white noise” meant “random signals through all the frequencies”.
A random number generator produces a sequence of numbers which is mathmatically related to white noise.
You can use a rng also to calculate intensities of points inside an image (the plain approach will result in what Grunnt has mentioned - TV “snow”). More interesting, there are applications of rngs which work like functions p = f(x,y), and give you a power value for a 2D point (or 3D point).
This way you can create patterns in 2D areas with such generators. By warping the coordinate space (x,y) and transforming the power values you can create a lot of different patterns.
More elaborate uses are that you can get a random vector for vecor as parameter like a function (a,b,c) = f(x,y,z). You can consider the (a,b,c) vecor a color (red, green, blue) for the point in space. But you can also see it as a field of wind or “forces” which fill the space (force vectors). You can use these force fields to create images through projections onto a surface, or let those force fields affect particles and planes.
It’s a big domain. Start looking up “perlin noise” for image applications first, that should be a good start.
Huh…I guess that local wiki page I’ve made isn’t very good at a background explanation. 
I’m not sure which page you mean, but the perlin noise page looks very good to me.
Edit: I suspect that the original poster just was confused why the term “noise” is used in conjunction with random number generators.
You guys really seem to suck at explaining things very simple, and for what you can use them.
(Sorry for language, but I think this mathematical approach is not the way to do that…)
Look at a noise picture again:
http://dl.dropbox.com/u/45530199/Programs/SimplexNoiseN/noise29.png
What you can see there is, that the picture consists of grey colors from dark black to light white.
Each pixel in that image is actually only a value between 0 and 255.
But as you can see this picture does not consist of somehow mixed colors, it consists of regions which tend to be white and regions which tend to be black…
It has somehow a regularity, which makes them so awesome.
The very simplest answer to your question would be: You can generate mountains from them, for example.
And I really think this answer is pretty straight-forward and a good answer. See this image:
The thing is: noise in the way you know it is used to create a big number of values, which look like they would create mountains. Think of each brightness in the image to be a number, which says how high a mountain should be at one point.
But noise is even more cool, you can use it to create explosion effects, lava textures, world maps, planet terrain (which is basicly the same as mountains, but more complex). Even minecraft uses noise to generate terrain.
Have fun exploring them and I hope this has helped you 