Edgar's pretty simple. He's the twenty-seven year old King of Figaro, and he spends most of his time preening and chasing after the hapless maidens of his kingdom. I mean, Figaro is bascially a desert; there ain't much to do. He's full of elegant fabrics and shoddy pick up lines, and his sprite winks and wags its finger with a brilliant and not very subtle panache.
But Edgar is complicated. He's the twenty-seven year old King of Figaro, which has been manipulated into an alliance with the Ghestalan Empire to insure its own safety. The same Empire that poisoned the previous king, Edgar's father, and the same Empire that Edgar has sworn to bring down by his teeth if he has to. So he covers his tracks and whispers his secrets and plans with the Returners all the ways the Empire could fall while laughing with his father's killer and doing all that winking finger-wagging nonsense.
Also, did I mention he's a super genius of Japanese RPG-level proportions? Yeah.All this might be easier if his brother Sabin hadn't up and left Figaro when theif father died. Edgar sacrificed his own freedom so that his brother could be happy, but he's chained to duty, crown, and revenge and he's chained alone. Well, maybe. Almost.
The person who understands Edgar best, the one he'd love to be able to confide in-- that's his long-lost twin. The person Edgar has is Locke.
Locke introduces Edgar as one of his Returner contacts, probably the only one in the area that has the real power neccessary to hide Terra for a while. He seems proud of knowing someone so royal, the nobody from the streets he is. But it becomes clear that Locke's not exactly in over-awe of his personage. They're friends. Good friends, at that.
Locke and Edgar have this banter that you only see a few times in the game, but there's still an element of familiarity to it. This is from Gau's makeover at the end of the game.
Edgar: This has to be it! Flair, style, a silk hat to top it off... rose between the teeth...
Locke: OVERDOING IT. Jeez... you really should have a bandana...
(Gau changes into a familiar vest, shirt, and pants, complete with forehead bandana.)
Edgar: How on earth does a bandanna say 'fine, upstanding citizen'? Not that I expect YOU to be, Locke, but--
Locke: What was that!? Say that again!
(Locke punches Edgar out. Fade to black.)
I feel obliged to note here that when Edgar disgueses himself as the thief-leader "Gerard" he does little more than steal Locke's color scheme. See?
But that's not the point. The point is that they know each other well enough to have a good laugh at the other's expense. The cast of Final Fantasy VI are largely strangers to one another, it's rare that we get to see them work past the formalities. But Edgar and Locke are just kinda fun together.
Edgar's also the only one who knows about Locke's past, and so knows the real reason he joined the Returners. He's also picked up on Locke's little hero complex, and warns Celes not to interpret his protectiveness as anything like love.
So see, they have this wonderful, funny, close relationship that isn't explored enough. Dammit, Square-Enix, when you inevitably remake this game, I want more Locke Edgar jokey fun time.