It just means that your family lineage, identity and history is determined by who your mother was.
Actually, Jewish custom is very similar.
As a famous Jewish commenter once said., it's 100% certain who your mother was - your father, not so much.
People from County Kerry are targeted with jokes of the blonde joke or Texas Aggie joke variety...at least they were when I was in Ireland.
The Jews only became matrilineal as the Diaspora; as a cohesive nation, they were patrilineal. Read the Bible.
It is an unfortunate commentary on both the uncertainties they suffered and the immoralities they indulged as exiles as they became increasingly atheistic (despite their superficial adherence to tradition).
Look at the typical “Jew” today: atheist, leftist, amoral.
Spare me the indignation: I took Hebrew class with a room full of Jews; they were all the above except for the teacher herself. I, the Gentile, and the teacher, an Israeli, were the only ones who knew anything about the Bible, and the only ones who did not subscribe to a vulgar and hedonistic lifestyle. Most of them had lived in a commune (kibbutz), and many of them were promiscuous.
(By the bye, my mother is part Jew. She, my siblings, and I would all have fried in Germany circa 1944. But she is a Christian, as was her very Jewish forbear - what they would now call a Messianic Jew.)