Although a lot of people use the terms Main Assist and Main Tank interchangeably, they are in fact two very different roles. Often the Main Tank is also the Main Assist, but the more difficult content we're raiding, the more often we will need to use two separate people for these roles. If you read the section about assisting carefully, you already have a good idea what the Main Assist's job is: to call assists on monsters. The Main Tank's role is different - to keep aggro on the monsters (in other words, tank them).
If the same person has both the MA and MT roles, they will usually grab a monster, wait a few seconds while they build enough aggro, and call assist.
If the MA and MT are different people, the main tank (and all other offtanks as well) will grab a monster and build enough aggro - and then someone different (the MA) will choose one of their monsters and call assist. The Main Assist will not grab aggro in this case. The raid will kill that monster while the original tank who grabbed the monster keeps tanking it. In this scenario, the offtanks are usually on the same level - so they are just tanks, and there may not be any Main tank or Secondary tank: all the tanks will be doing the same job - i.e. occupying the monsters.
In the latter scenario, Main Assist can be pretty much any class - usually one of those who rarely need to target anything else than the monsters.