The Prusik (or spelled prussik) is the most basic friction knot used in climbing and mountaineering. It can be used for self-belay and for progress capture (eg during rescue situations).
Similar knots include the Bachmann Knot, Klemheist, and Autoblock; there are other friction hitches such as Blake's Hitch that may be useful in similar situations as well. The prusik is notable because it is bi-directional (it will hold in up and down directions) and has very good grip. The main downside is that it easily tightens, and is difficult to slide up. Alternatives include the knots mentioned earlier (Bachmann,...), or static (e.g. the Petzl Tibloc) and dynamic (e.g. the original jumar, or modern versions) mechanical ascenders.
The prusik is used for tying a smaller rope or cord (typically, between 5mm and 8mm, with 6mm and 7mm being the most common) around a bigger rope (usually 9mm to 10.5mm).
Bluewater rope company makes some cord specifically designed for prusiks; this nylon cord is dynamic (like a dynamic rope), whereas most cord under 8mm is static. The cord is also designed to be flexible and thus allow tighter knots. They have 6.5mm, 7mm and 8mm cord. The 6.5 mm cord is an ideal diameter for prusiks.
The knot is very simple to tie: it is similar to a girth hitch, but with more wraps. It is typically tied with 2 or 3 wraps. More wraps will give it more holding power. If the thicker rope is relatively skinny (e.g. < 10mm) or if it is icy, the prusik will not hold as well, and you should have at least three wraps.
The term prusikking up a rope is jargon for ascending a rope.
From wikimedia commons:
These pictures show prusiks with 2 wraps (that is, 4 wraps total since it is symmetric). We recommend 3 wraps (that is, 6 wraps total) for mountaineering, or even 4 (8 total) for ascending a thin line. http://upload.wikimedia.org/wikipedia/commons/a/ae/Prusik.jpg http://upload.wikimedia.org/wikipedia/commons/thumb/5/50/Nodo-prusik.JPG/450px-Nodo-prusik.JPG