You can spend inspiration in two ways
1. You can give it to someone else for being awesome. So if Fred pulls off an awesome stunt, you can throw Fred your inspiration.
I recommend spending it quickly, so you'll be able to get it again next time you roleplay a flaw, trait, bond or flaw.
I use nice big fantasy coins to represent inspiration, so they are clearly visible and easy to remember, and make the "economy" aspect more tactile.