The stack pointer (SP) in an 8051 microcontroller is responsible for tracking the current position of the stack that is used as scratch memory. SP points to the last used location, and when data is pushed onto the stack, SP is decremented or incremented by 1 depending on the feature of different versions of 8051. The instruction PUSH not only saves the contents of register(s) onto the stack but also increments SP by 1. The 8051's stack pointer is important in providing efficient ways for controlling program flow and making conversion between data types easier.