On a boat with a shaft-driven propeller, the shaft leaves the hull at an angle and runs some way through the water before the propeller. The P-bracket holds its outer end, close to the propeller. It's shaped like a P, or an A with two legs, and carries the cutless bearing. Americans usually call it a strut.
It takes the propeller's thrust and all its vibration. If its base or fastenings work loose, the shaft runs out of line and the hull round the base starts to flex.
What a surveyor checks
With the boat hauled, load the propeller by hand, up and down and side to side, and watch two things. Movement of the shaft in the bearing is bearing wear: Good Old Boat's Bill Sandifer calls more than 3/16 inch too much. Movement of the bracket on the hull is this problem. Look round the base for cracked gelcoat and weeping, and inside for the fastenings: PBO's Stu Davies notes the bottom bolt as the issue on one boat.
In the report
"P-bracket, moves visibly on the hull when the propeller is loaded by hand, gelcoat cracked round the forward leg. Withdraw the shaft, rebed and through-bolt the bracket, repair the laminate, check alignment." See loose P-bracket.