Hot Swapping refers to inserting or removing a circuit card from a powered backplane. The circuit card presents an almost dead short to the supplies on the backplane with the discharged capacitors (bulk filtering, bypass, and hold-up). This dead short can cause a power-dip or brown-out on the backplane which can result in a series of resets to the other cards already in the system. A hot swap controller limits the inrush current to prevent the power-dip by modulating a series MOSFET based on the measured current. The following reference designs explain this concept in greater detail:
RD1057 5V and 3V Hot Swap Controller