I'll admit it, I was a bit leery about 5E's Inspiration mechanic. To me it seemed like it was either...
...a munchkin tactic wherein the players would work to get them for no reason other than to gain a numerical advantage in game.
...an unnecessary rule that overcomplicated the system.
...virtually the same as the Advantage/Disadvantage mechanic.
However, having seen it in practice I've decided I like it.
The munchkin, min/maxer, in my game quickly started going for it. He started role-playing the quirks on his character sheet (the players are using the pre-gens from the Starter Set while we try out the system). The thing is, he is not the most diligent role-player. He is very based in the numbers and not the character. I would call him a roll-player and not a role-player. And yet, here he was role-playing and doing it well. Sure he was doing it to gain the advantage for his die rolling, but despite the motivation...he was role-playing!
The best part was that he was interacting more with the other characters and getting them to role-play as well. While my fear of munchkin-ism was basically proven true, I'm okay with that. The end result is an overall improvement to the game.
The second Inspiration I handed out was when one of the players made the entire table roar in laughter for a good long time. I'm not even sure if it was for something in-character or out-of-character; it didn't matter. It seemed like a nice reward for entertaining us and she seemed pleased to get it.
For me, Inspiration is a reward for role-playing or simply being entertaining. It's a way to reward the players when they do something I approve of, a way to give them direction without demanding it. I'm liking it utilization.