Well, out of what happens in Revenant Wings, there's a few things you should know. In one scene (you might've seen it) they reference how they destroyed the Sun Cryst. The Sun Cryst was the source of nethicite, a huge crystal-like source of energy, derived from the "gods", that was the origin of deifacted nethicite - stones that could unleash massive power. One had to cut a shard from the Sun Cryst and that shard would be nethicite.

About relationships, Vaan is the main character in both, Penelo is a chick he grew up with/lived with after his parents died. Sometimes their relationship is implied as platonic, at other times it's not. Balthier is Vaan's personal idol, someone he looks up to very much. Fran's Balthier's partner and it's never disclosed as to what their exact relationship is, although there's some hints that its possibly romantic. There's some hints at Vaan having romantic interest in princess/now queen Ashe, and at some parts it seemed mutual. Balthier also seems to attempt to throw some lines at her. Vaan's brother fought under Basch in the battle he died in, Basch is someone who Vaan learns about knighthood from, as opposed to skypirating from Balthier. Larsa is heir-apparent of the Archadian empire, the bad guys in XII, although he was always a close ally of the main party, yet he also seems to have a thing for Penelo.

The Occuria are also referenced - they are undying beings ("The Undying") and self-proclaimed gods of Ivalice, although after the events of XII, their sovereignty is mostly undone.

If you played Final Fantasy Tactics, there's something from the updated War of the Lions version you should know - the Auracite are the Zodiac Stones.