Kangaroo is right.
Web applications (such as IE) can use a little of both, though. HTML, cookies, picture files, and all the stuff that is loaded to your machine, is run from RAM. The web-browser itself, and the actual "drawing" of the pictures and viewing of the HTML, is done by your graphics card. The graphics card does its work on its own memory (unless it runs out, then it starts grabbing system RAM).
In today's world (especially if yer running WinXP) you should have no less than 512mb RAM, and yer video card should have no less than 64mb (though 128 is becoming standard).