A pseudorandom signal lets you overlay many signals on the same frequency.
If you've got the same sequence in your receiver as a pseudorandomly hopping transmitter, you know when and where to look for the signal. You get a statistically significant amount of information despite the channel being noisy. That noise also includes all the other pseudorandom signals, which you won't get a statistically significant amount of energy from - everyone on the same channel with a different pseudorandom sequence will think that, in effect, they're the only one there.
There'll be occasional collisions - and the more channels on the same frequency, the more collisions you'll get, so it's not a free lunch - but you can treat other signals as so many decibels of noise to include in your link budget. You can do all sorts of things (some of which GPS does) to increase your gain over noise too.
Why pseudorandom? If the signal you were listening for was truly random, you'd have no hope of finding it. If it wasn't random at all, then you'd get all sorts of effects when you and the other users on the channel were in sync (although you can do it that way - it doesn't work very well, mind).
There _are_ security uses for pseudorandom signals: with care, you can establish a useful channel which is well beneath the ambient noise in a channel and thus not visible to someone trying to detect, intercept or block you (up to a point: the more you know about the signal, the more you can do even without the sequence).
But in the open GPS service, the pseudorandom stuff is primarily there to share spectrum effectively. There's no secret stuff.
If you want to know more about this, look up CDMA (Code Division Multiple Access) - it goes alongside FDMA (Frequency - where you get your own channel) and TDMA (Time - where you get exclusive use of a channel for a slice of time).
R