Well to START with, you kind of have to be a big Whedon fan in the first place (which it sounds like the OP probably isn't). You have to like his style of dialogue, the way he writes his characters, etc.
And even then, it still took 3 or 4 episodes for the show to really click with me.
Well, I wasn't. Firefly was my first real exposure to Joss Whedon. I've since come to enjoy most of his stuff, though.
Firefly is chock full of quotability. Oddly, though, one of the most memorable exchanges is one which doesn't get pulled out all that often:
Mal: "Cattle on the ship three weeks, she don't go near 'em. Now we're on Jiangyin and suddenly she's got a drivin' need to commune with the beasts."
River: "They weren't cows inside. They were waiting to be but they forgot. Now they see sky and they remember what they are."
Mal: "Is it bad that what she said made perfect sense to me?"