Overtiredness is the state a baby reaches when they have been awake longer than they can comfortably manage. Counterintuitively, an overtired baby does not become easy to put down; they become wired, fussy and much harder to settle, and their sleep after tends to be short and broken.
It is one of the main reasons a nap or bedtime falls apart. Once a baby is past the window where they could drift off, sleep becomes a fight.
The whole game is prevention. Watch your baby's tired cues and keep to sensible wake windows so you offer sleep while they are calm and drowsy. With twins this matters twice over, because settling two overtired babies at the same time is one of the hardest jobs there is, and it is largely avoidable.