As michaelr has said, the "monitor" function on a stereo amplifier allows you to listen to (techie term: to "monitor") the sounds from your tape recorder, while the recorder itself is recording the program supplied by the "tape out" connectors on the amplifier -- probably selected by the "program" switch". This gives you a way to confirm that the recorder is working properly.

Your amplifier is apparently set up to work with two separate recorders -- Tape 1 and Tape 2 -- and so it has separate monitor switches for each recorder.

On the back of the amplifier, you will see connectors marked "Tape 1 In" and "Tape 2 In." When you push the Tape 1 Montor button, you will hear the machine connected to Tape 1 In; when you push the Tape 2 Monitor buton, you will hear the machine connected to Tape 2 In.