"The cut" is anyone more than 10 shots behind the lead score after the end of the second round. E.g leader is on -8, anyone up to +2 gets in. +3 or worse and you're out.
Sorry el_dazzer, you're wrong (kind of) and yes, Merlin5, you are right. Imagine the uproar if the leader was at -10 after day 2 and the nearest competitors were at +1, would that mean we just give him the trophy and not play sat/sun as only he would make the cut?
From the masters website:
In 1957, the 36-hole cut was instituted. The low 40 and ties and those within 10 strokes of the leader would qualify for the final 36 holes. In 1961, it was changed to the low 44 and ties (and those within 10 strokes of the leader).
This ensures that 'at least' 44 players will make the cut who will then make the minimum 22 pairings required. The 10 shot rule then allows more players to make the cut if they are within 10 shots of the leader.
/edit: This is also true i believe for other US based majors due to the smaller number of entries compared to a normal event. For The Open the 10 shot rule is not used and it is low 44 and ties.
The cut for most PGA TOUR events remains at low 70 professionals and ties. If that cut results in a field larger than 78 professionals, the cut will generally be at the next lower score, meaning the weekend field will be smaller than 70. In a very few cases, the "number nearest 70" may still be over 78 (i.e. 80 players Vs 59), in which case the larger number of professionals would play the weekend.