A counterpoint consists of two or more independent contour melodies, they are rhythmically and harmonically independent. A counterpoint has five different categories: First species, second species, third species, fourth species, and fifth species.
Explained in brevity, here are the following examples:
1) First species counterpoint
A first species counterpoint is a note-against-note melody. An example of this is provided by Guitarslinger.
2) Second species counterpoint
Second species counterpoint is two notes-against-one note. For example, if one voice plays a quarter-note, the second voice will play two eighth-notes; two half-notes plays against one whole-note.
3) Third species counterpoint
Third species counterpoint is three or four notes against one note. For example, one voice will play a quarter-note and a second voice will play four sixteenth notes against the quarter-note; or one voice will play four quarter-notes against one whole-note.
4) Fourth species counterpoint
This is where counterpoint gets fun. It's when notes are offset against each other and it creates a dissonance, usually on the beat. It is possible to have dissonance on the first measure, as long as the dissonance is prepared and resolved. To create this dissonance in fourth species counterpoints, the notes are sustained; it helps produce this as well as a sense of syncopation.
5) Fifth species counterpoint
In a nutshell, fifth species counterpoint is all of the above examples composed into one form. It is the closet one can get to a "free" counterpoint.
A number of examples of counterpoint can be found by J.S. Bach
Here is an example:
"Little" Fugue (G minor)
http://www.youtube.com/watch?v=pVadl4ocX0M
In particular, this is a fugue, in which a short theme is presented in the beginning and is imitated by three other voices, and it appears throughout the piece.
It is pretty cool stuff, I love polyphony. =]
Hope this helps.
All images are taken from en.wikipedia.org/wiki/counterpoint