I wonder what is exactly the work of the middleman

Well middleman is a guy who helps in a trade that may have some risks.
Example there are 2 guys that wants to trade with each other, one has 1 steam code or paypal money and the other guy has steam gift or whatever, and there is a problem which is going first. The middlemen keeps the gift of the second guy in his inventory while the other guy gives the money/steam code, and if the money goes to him or steam code works fine the gift that was on the middleman's inventory from the second guy goes to the first guy, since the codes worked/paypal moneys sent.
You can find a middleman at steamrep.com, and no he does not get anything expect a "+rep trusted middleman" or something similar on his profile comments.
Hope i helped you.

Hmm, I always thought it was like, both trade to MM and then he trades with the corresponding people, no? (Give why MM need high reputation)