Well,
Counterpoint is where the song is not so much made up of chords and melodies but more where each part has an independant melodic line that when played with the other lines set up the harmonic content.
from wikipedia
In music, counterpoint is the relationship between two or more voices that are independent in contour and rhythm and are harmonically interdependent. It has been most commonly identified in classical music, developing strongly during the Renaissance and in much of the common practice period, especially in Baroque music. The term originates from the Latin punctus contra punctum meaning "point against point".
http://en.wikipedia.org/wiki/Counterpoint
As a modern bassist it would almost compare to a walking bass line that while being its own melodic line also takes motifs from the vocal or lead instrumental melody.
Hope that helped a little.
john
