Undertone got it, but i'm going to add alittle...because i'm a pompous asshole. Vector art doesn't use a pixel grid, therefore printed images can be made to the maximum capabilities of your hardware. Also, it's interely scalable. I can print the same Illustrator design at 2"x2" or at 200'x200' and it'll be the same clarity on both. The scaling is really really important for logos.
If you never do printed work then you'll probably never have the need to use illustrator. Those of us in the design industry though, use it all the time...and grow to love it.