I was searching for how to create a 2 dimensional n-body simulation (triggered by my "why is stuff flat" thread), and on a youtube video, this guy basically said "n-body problem, verlet integration, and barnes-hut algorithm"
(video in question). I had no clue what the second two were, so I googled. I couldn't really wrap my head around the explanation (of verlet integration) on
wikipedia, so I googled more (I even googled with bing XD)
This article cleared up everything and then some:
http://www.gamedev.net/reference/programming/features/verletPhys/default.asp
Not only does it make it easy to see what verlet integration, it also discusses verlet, vertex-based objects, and talks about collision detection and response, vertex movement, and rotation.
The first two images on that page cleared up a lot with me. Basically, the common method is called "Euler Integration". You take a step in your program, move your objects, take another step, etc.

(everything being a vector except for the scalar timestep).
opposed to verlet integration:
There's even a
demo of everything the guy talks about.
Really awesome article.
[edit]
euler integrations and verlet integrations are not accurate to the actual path objects would take. Look at the images on this page:
http://en.wikipedia.org/wiki/Euler_method