The "pin levels" are saved in the stack. But the pin levels are probably affected by the value you wrote in the output latches earlier.
There are some fancy uses of the pair push pop:

Example 1: Force 0s in the P1 pins that are 0s at push time.
push p1 ; 'save the pins'
pop p1 ; write the latches

Example 2: echo in the serial port
push sbuf
pop sbuf

As a rule: push is a read operation, as Erik said, and pop is a write operation.

Regards,
Alfredo del Rio