Cup
The cup is the hole in the green into which the ball must be holed — colloquially also the word for the flagstick.
The cup is the target of every hole: a recess in the green with a diameter of 108 millimetres and a depth of at least ten centimetres. All rule definitions around holing out are embedded in this standard. The ball is holed when it rests below the edge of the hole and is held by the hole. The term is used two ways: when people speak of the "cup", they usually mean the hole itself, but sometimes also the flag in it.
In practice you encounter the cup mainly when putting and during course maintenance. Greenkeepers move the hole regularly so that the flag position changes and no wear ring forms. Example: yesterday the flag was front left, today back right behind a bunker. Your approach has to adapt, otherwise you face a ten-metre putt over the ridges. When holing out you pull the flag or have it attended; since 2019 the ball may also be holed with the flag left in.
A typical misconception is the lip-out question. If the ball bounces back out at the edge of the hole, it does not count as holed, even if it was briefly in the cup. It has to rest in it. A ball that is resting on another object inside the hole and does not lie completely below the edge also does not count. The rulebook regulates the details; in everyday play it helps to look at the frequently asked questions on the subject of holing out.
FAQ
May the flag stay in the hole while putting?
Yes, since the rule reform of 2019 you may hole out while the flag is in the cup. If the ball strikes the flag, there is no penalty, neither from the green nor from off it. Whether you want the flag pulled, attended or left in is purely a matter of taste and depends on what you feel safer with.
Does a ball count as holed if it bounces back out at the edge of the hole?
No. The ball is holed only once it rests below the edge of the hole and is held by the hole. If it bounces back out after lipping in, it was never properly in the hole, and you must keep playing. A ball hanging on something else inside the hole and not lying completely below the edge does not count either.
Why does the flag keep moving around on the green?
The greenkeepers move the cup regularly so that the flag position changes and no wear ring forms around the hole from the many footsteps. For you that means: your approach has to adjust to the position anew every day, otherwise you face an endless putt over the ridges.