While in photoshop it sounds like you're removing the background that you don't want, in illustrator you'd draw the parts you do want. The result would be an infininitely scalable version of the artwork (vector). Here's a good tutorial.
You're working with anchor points. Like dot to dot. Illustrator uses mathematical vector as opposed to Photoshop's raster process which takes in all the pixels in the image.
It's a smaller file but the advantage is as Kurd said is an infinitely scalable image.