Trade section allows you to trade your own pokemon with another trainers. You can use connectors AND/OR, to specify which kind of trade do you wish, by using AND you're saying that you wish all the pokemon that you requested, and by using OR you say that you wish one of the requested pokemon.
For each traded pokemon you can demand up to 3 groups of pokemon 3 pokemon (every group is linked to the others by the connection OR, and it's composed by pokemon connected with AND) , e.g, for a riolu, you could demand [pidgey AND ratatta shadow AND gastly shiny] OR [zubat AND haunter AND Any shadow] OR [gengar shiny]. Note that you can also specify what kind of pokemon do u wish (regular OR shiny OR shadow). If you don't make any demand, you'll have to manually accept the trade (when it has requests)
If you offer all demanded pokemon, the trade will be instantly completed; e.g, for the riolu said before you could offer a shiny gengar and you would get it. If you don't offer all demanded pokemon you'll have to wait to the answer of the another trainer, meaning that the trade could be accepted or denied.