I agree there's no pressing need to know about various types of noise in order to record--but there's nothing wrong with a bit of curiosity. Similarly, if you Google "white noise" and "pink noise" and so on, many of the results are badly written or difficult to understand.
So...now's my chance to write something equally badly!
What is noise?
There are lots of things that can be considered noise in terms of an audio signal--hum, buzz, clicks and so on. However, what we're talking about here is purely random signal with all audio frequencies present (over time). To get complicated, it's generated by random thermal motion of electrons. When the noise is at a high enough level, we perceive it as a hiss--like we hear when a radio isn't tuned to a transmitting station.
White Noise
White noise is the simplest form of this random noise. Every frequency (Hz) is at exactly the same amount of energy. However, this is a bit of a problem if you want to use the white noise to calibrate things. The span from 50 Hz to 100 Hz is one octave; 100 Hz to 200 Hz is another octave and so on. At higher frequencies, 10,000 Hz to 20,000 Hz is also an octave. Since every frequency has identical energy, you can see that the energy level for an octave is higher each time the frequency goes up. I don't know if you've played with the maths of dB measurements but this means each successive octave is 3dB louder than the one beneath it--meaning that the noise will sound kind of harsh and "toppy". Displayed on a frequency graph, white noise will be a diagonal line running upwards from left to right.
Pink Noise
Pink noise starts off exactly the same as white noise but is passed through a filter (believe it or not, called a "pinking filter"). What this does is know the energy down by 3dB per octave so every successive octave has the same amount of energy. Displayed on a graph, this'll look like the kind of flat line you want when you check the specs of a mic or speaker. (Yeah, yeah, I know that some subtle peaks in the right place can make a mic or speaker sound better subjectively but you get my drift.)
Once you have the same energy per octave, the noise becomes useful for the alignment and calibration of gear, particularly speakers. When I'm setting up
a live sound system, I'll play pink noise through the speakers and analyse the frequency response with a "real time analyser". This gives me a display of the frequency response coming from the speakers and any diversion from a straight, flat line can be balanced out using equalisation.
That said, the pink noise and RTA only give a starting point. What can look perfect on an RTA can still sound like rubbish--listening to real music and making is sound good is still the final stage of a set up.
Brown Noise
...just to confuse you, has nothing to do with the colour Brown. It's named after the scientist Robert Brown who discovered Brownian motion--and it's noise created by exactly that. It has no real application in audio work (at least not outside test labs) but, if you're interested, is noise where the energy REDUCES as the frequency goes up, this time by 12 dB per octave.
Dang. I can see why so many Google hits make this all seem complicated. It's hard to both keep it simple and keep it accurate at the same time.
Anyhow, hope it helps.