The answer is "it depends." I
f the barn owl is independent (no nesting mate or owlets), it will only hunt a rodent or so per night to sustain itself, depending on the size of the prey. If the "barnie" (as many owl appreciators call them) is feeding a mate and a nest full of owlets, it's going to hunt day and night if necessary (yes, they'll hunt during the day if necessary).
The hunting trips per night will increase as the owlets grow from sharing bits of one rodent to each consuming its own - by that time both parents are out hunting.
The quantity also depends on the size of the prey. A small rabbit could feed a nest of four for a night but it would take a half dozen small mice to do the same.
Barn owls will also store food for later, as they cannot always depend on a successful hunt every night, especially in areas prone to flooding or other natural phenomena.