Matrilineal is a way of reckoning descent by mother's status. Which means that all of your legal and social status comes from whatever status your mother has.

In most Western societies, currently, descent is reckoned patrilinealy since babies get the father's last name, although since in most Western societies, people don't officially inherit social status, it could be said that we are neither patrilineal or matrilieal.

The most common example of matrilineal descent in the modern world is the Jewish people. A Jew is considered a Jew if they have a mother who is a Jew. However, Jews do adopt their Father's last name, not their mothers.

The issue of Jewish matrilineality brings up the issue of The Matrilineal descent of the Jewish people.

Why would a culture be matrilineal? (This question may not seem important, but go read Avunculocal residence. You'll start to wonder). Matrilineal societies don't usually give more power to females, so why determine descent through them?

There isn't one single answer for all societies, but in some cases the answer is simply that the babies come from the mother's body. In some cases, the father isn't seen as having anything to do with the creation of the child.

If you know another explanation, please post it.