The main inserts work similarly to channel inserts, except that they are usually stereo (2 physical jacks, left and right) instead of mono (single physical jack). An insert allows you to send the channel's signal OUT and back IN to the mixer jack from one 1/4" jack. In the case of the stereo main inserts, the left main insert would "send" the left channel of your main mix OUT to the input of a processor - say an EQ - then the "return" from the EQ's output would route the signal back into that same 1/4" jack on the back of the mixer. The signal would then pass out of the mixers MAIN outputs with the EQ processed sound. They call them inserts because you are literally "inserting" the device into the middle of the signal chain at one point. This connection allows you to patch in effects that require a complete wet signal without the presence of the dry (original)signal. Such effects include - but are not limited - to compression and EQ.
You will need a special send and return cable, aptly called an "insert cable" (see picture). Take care not to confuse this with a "Y" cable... though they look similar, a "Y" cable usually has 2-conductor TS connections or 3-conductor TRS connections on all plugs. An insert cable, on the other hand, ALWAYS has one 3-conductor TRS plug that splits into two 2-conductor TS plugs - a "send" and "return".