The term "in bounds" is synonymous with the "field of play". This is the length of the field from the back of one team's end zone to the back of the other team's end zone and the width of the field from sideline to sideline.
In the NFL the field of play is 120 yards long (100 yards from goal line to goal line and 10 for each end zone) by 53.5 yards. This is important for several reasons. When a receiver is catching the football, he must establish control with both feet in bounds for the catch to count. Contact is only allowed to be made in bounds; any contact out of bounds is a personal foul penalty.