What should I know about the previous MI franchise before watching MI: Fallout?

I would say you could watch it without knowing anything about the previous films. There isn't much continuation from the previous films. What little there is is pretty much explained.

Although, the biggest plot point is the origin of the Apostles who are the main antagonists of MI: Fallout.

Spoilers for MI: Rogue Nation and small spoilers for MI: Fallout

At the beginning of Fallout, the Apostles are introduced as a terrorist-for-hire organization which spawned from The Syndicate. The Syndicate were the main antagonists of MI: Rogue Nation. They were lead by ex-MI6 operative turned anarchist Solomon Lane. They are comprised of rogue operatives of the various government spy organizations (CIA, MI6, etc.), which makes them very skilled and dangerous. They operate much like those agencies and seemingly have the same resources. In Rogue Nation, their stated goal was to bring down the world's governments. Ethan Hunt of course manages to stop their plans and capture Solomon.

Another recurring character from Rogue Nation is Ilsa Faust. She was a member of the Syndicate. Though her true loyalties lie with MI6, and she helps Ethan stop Solomon and the Syndicate. Her and Ethan have a romantic relationship (or as much as two spies in this world can have) before splitting apart at the end of the movie.

Aside from that, there are Ethan's allies. Intelligence operative Benji Dunn and computer specialist Luther Stickell. Though you don't need to know much about them other than they are Ethan's main go-to guys throughout the series.

There is also Alan Hunley who acts as Ethan's superior. Often the guy who yells at him a lot, but sticks up for him in the end.