Independent in rhythm & contour means that the voices may have different rhythms and contour, respectively.
For example, if a voice goes up and another goes down, the voices would be moving in opposing motion. Moreover, one voice may be going up, and then down while the other remains going down only. All this means that the voices are independent in contour.
Independent in rhythm is analogous; the rhythm of one voice doesn't affect the rhythm of the other voice.
On the other side is harmony. Unlike rhythm or contour, each note being played at a time has a role on the harmony. Then, the harmony is dependent on each voice.
Counterpoint, in simple terms, is a technique for creating "good" harmony with independent voices (independent on contour & rhythm). Another way of looking at it is: Counterpoint is a technique for composing various simultaneous independent voices without messing up the harmony.