Tip-up carry means the knife sits in your pocket with the blade tip pointing upward, toward the pocket opening. It is the faster orientation to deploy from, and it is the more common setup on modern folders.
Drawing tip-up puts the knife into your hand in the same orientation you will use it, so your thumb lands on the stud or your finger on the flipper with no repositioning. Tip-down requires a shift.
It is also the only orientation a flipper really works from, which is a large part of why modern folders default to it.
The traditional argument against tip-up is that if the detent fails or the knife catches on the pocket, the exposed edge faces the pocket opening. In practice modern detents are strong and this is rare, but it is the reason some people still prefer tip-down.
A worn detent is the real risk. If a tip-up folder starts opening in your pocket, stop carrying it that way until the detent is fixed.