Foul ball
 

Can anyone explain what "boxing in a foul ball at the fence"is?

Our director stated that he had observed umpires not doing this.

This refers to chasing a foul ball that goes towards a fence for a possible catch/no catch scenario. Both the plate umpire and 1st base umpire, if the ball is down the right field line (or plate umpire and 3rd base umpire, if the ball is down the left field line and there is a 3 or 4 umpire crew) converge on the area where the foul ball is coming down (near a fence, in this case), and watch the fielder attempting to catch the ball. The umpire to whom the fielder turns will make the catch-no catch decision, and the other umpire will determine if the fielder was in live-ball territory when the catch was made, or if there was interference with the fielder. Because the umpires converge on the scene around foul ball, they are boxing in the play. This is what your director most likely referred to.

Some people call it bracketing the foul ball instead of boxing it in. There is a section on it in the USA Softball Umpire Manual, page 61.

USA.1803 Umpire Supplement FINAL2-HIREZ

Just one correction, and that's that the ball is somewhere between home and first base or third base. If the ball is further down the right or left field lines, the PU has no responsibility to make that call unless his/her partner doesn't chase, or is not in position to chase.