A camera stabilizer is a mount for a video camera which mechanically isolates the camera operator's movement from the camera. This allows a smooth shot even if the operator is moving quickly over an uneven surface.
Using a stabiliser gives you the benefits of a normal static tripod with the fluid motion of a dolly and the flexibility of a hand-held shot. The purpose of the stabilizer is to follow the operators intended movements while absorbing unwanted jerks, bumps, and shakes.
The original and most well known camera stabilizer is the Steadicam invented by Garrett Brown.
If an original Steadicam is outside of your budget (and if you are reading this then it almost certainly is!) then there are number of cheap alternatives for the low-budget film maker.
How To Make a Camcorder Stabilizer By ToddSeda
Making a Camcorder Stabilizer by John Beale
Build Your Own Steadicam-type Stabilizer for the XL1 by Chris Santucci
$14 Camera Stabilizer by Johnny Chung Lee
Homebuilt Stabilizers with lots of photos!
Homemade camcorder shoulder/pistol grip stabilizer By cinemasteve87
Which stabilizer you build or how you modify it depends on your use. You may need a few different designs and use them appropriately.