A very misused term in amateur radio it seems. For instance when I was researching how to put up my random wire antenna I came across a recommendation to use a "counterpoise" of equal length to the random wire but attached to the shield side of the coax feed line and placed below the main antenna. This actually just makes the antenna a dipole (more or less) but with each leg parallel and close together and of "random" length. Another common misuse is to call the "tiger tail" that many add to HT antennas a "counterpoise."
I didn't know any better until recently when I decided to better understand what it was and was not. I'll let the reader discover it's real meaning and most common misuses in the following articles:
Counterpoise? (by L. B. Cebik, W4RNL)
Counterpoise (VK1OD on the 'net)