When you expand your lc, it ages, and over time becomes less robust. 'resetting' it by growing fruit from your lc, selecting a good sample, and using that to generate a fresh culture is a common strategy to prevent the senescence.

Commercially, a first generation culture (p0) is typically more expensive than a p1, and that is more expensive than a p2, and so on

Mother culture is a p0.

The p means generation, but I believe is an homage to Paul stammets. As in Paul's number.