As humans, we're not naturally inclined to play music in time. Our speech while rhythmic at times is vastly more complicated rhythmically than the majority of music out there. Just check out this article by Steve Vai in which he talks about polyrhythms. He talks about how one of the toughest challenges he has ever faced in music is transcribing speech.
But what does this have to do with metronomes?
I'm glad you asked, other Alex. Well, our minds and ears are flexable to the complicated sounds of the world. We're not naturally used to the constant pulse of set tempos. Our heartbeats are variable, and slow and speed in phases, and there's not really that much in the natural world which exerts a constant audible tempo. So, when we try to play a steady tempo without a metronome, what we will actually do is slightly speed up, slow down, and compensate when we fall behind the beat. As soon as a group of musicians trained in such a way gets together, everyone will be in time with themselves, and out of time with others(I've been there, it's not pretty).
Enter the metronome.
The metronome is constant, unyeilding. It does not forgive, it does not forget. When you play 50 ms out of time and there's a metronome there, you can hear the difference, and it's not the metronome's fault that you were out. Playing to a metronome makes you consistent. It makes every one of the people playing along consistent, and it enables players to develop a sense of timing to use while they play with themselves and each other.
It can also help you with playing faster, and more accurately quicker, see these questions:
Technique or exercise to play this part from a song which i'm stuck with
I find myself making the same mistake when practising - despite focussing on that part- how to remedy?
As a parting note I'd say I never used to practice with a metronome, and my skill went up rapidly as soon as I started doing it. Getting into the habit of practicing with a metronome is a huuuuuuuuge benefit in both the short and the long run.
Hope that helps :)