Matriliny is the practice of following one's ancestry through the female line.
As tribes had to be fairly small for their surroundings to support them, mates were normally outside the clan at seasonal gatherings. It is uncertain if these were temporary or permanent bonds. However, as tribes were regularly moving in different directions there would have been no guarantee that the two tribes of the couple would ever meet again.
The male participation in reproduction was unknown in the paleolithic era, so that the only connection a child knew about was through the mother. It only made sense, then, that a marriage involved the male migrating to the female's tribe.