What is the press-repress system of golf scoring?

Answer 1

It is a repeat bet made typically in a Nassau format match.

(Nassau is a match play 3 wager system, where the front-9, back-9, and overall are each a separate wager).

This article should explain everything:

Answer 2

some people play two down automatic press. That means everytime someone goes two holes down on the original bet another one starts.