When I am coming up with a story and the characters, if I don't have the full story worked out yet, I start to think about the background of each character. What lead them to the point where they are and made them who they are. What happened to the world they live in or the area in which the game takes place. For me thinking about these aspects will actually help solidify and fill in the gaps in the original concept. Knowing these pieces can help fill in the "why" of your story which will help you lend context or reason the "how". Not only for your protagonist but also for your antagonists, the enemies and other characters in your story and not just the hero.
If you put some thought into why the enemy are doing what they are, or what led them to that point, it will often help you come up with many other pieces like behaviors, abilities, reactions, and even deciding on bosses, etc...
I like to think about these things when I am first working on the concept of the game as it really helps solidify a lot of your mechanics and gives you a much clearer picture of what you want to create. The more fully you can envision what your game world is, the more tools you have for bringing it to life and actually finishing the product. There are few things harder then finishing a game design when you don't fully have the concept fleshed out in your mind already.
Take notes, test, experiment, then do it again and improve it. I am a firm believer in iterative design. Build it, and then either rebuild it or build onto it. Better and more concrete each time. Just a thought... Just my 2 cents...