There is no commonly accepted definition for a TP monitor. According to Jeri Edwards' a TP Monitor is "an OS for transaction processing".
TP Monitor does mainly two things extremely well. They are Process management and Transaction management.
They were originally introduced to run classes of applications that could service hundreds and sometimes thousands of clients. TP Monitors provide an OS - on top of existing OS - that connects in real time these thousands of humans with a pool of shared server processes.
TP lite, based on stored procedures.
TP heavy, based on the TP monitors.