'ring off the hook' has a few meanings. eg it can mean for a telephone to ring incessantly and repeatedly.
eg What a busy day! The telephone has been ringing off the hook all day long.eg The telephone has been ringing off the hook ever since the ad appeared in the paper.
'ring off the hook' is also an informal way of saying that the phone rings a lot. eg The school office phone was ringing off the hook all day
It also means to receive an extremely large number of telephone calls The office phones were ringing off the hook all day.
The etymology of this expression is based on the idea of having the telephone ring so much it causes the part you hold in your hand, to fall off the part it rests on.