The first ball screen does not get anything, so the screener turns and sets it again on the other shoulder. The handler takes one dribble back the other way and uses it. Nothing new has been added to the possession except a second chance.
Why coaches use it
It is the cheapest counter in the book. No extra personnel, no new spacing, no second call.
It works because defenders are at their most vulnerable while recovering. The guard who fought over the first screen is still getting back to the handler’s hip. The big who dropped is still retreating toward the rim and now has to change direction. Hit them in that window and the second screen produces what the first one did not.
The naming is not settled. Many staffs say re-screen when the same man sets it twice and twist when the second screener is a different big taking over from the first, going back the other way. Others use the two words for the same thing. Pick one and be consistent, because the call has to be understood in a timeout.
How it is guarded
Talk, mostly. The on-ball defender needs an early call so he can beat the handler to the second screen rather than chasing it.
A team playing drop can survive a re-screen if the big is disciplined about retreating to the middle of the floor instead of following the first action. Teams that hedge or switch have a harder time, because the recovery from the first screen is exactly what the second one attacks.