Inspiration is a rule the game master can use to reward you for playing your character in a way that’s true to their personality traits, ideal, bond, and flaw. By using inspiration, you can draw on your personality trait of compassion for the downtrodden to give you an edge in negotiating with the Beggar Prince. Or inspiration can let you call on your bond to the defense of your home village to push past the effect of a spell that has been laid on you.
Your GM can choose to give you inspiration for a variety of reasons. Typically, GMs award it when you play out your personality traits, give in to the drawbacks presented by a flaw or bond, and otherwise portray your character in a compelling way. Your GM will tell you how you can earn inspiration in the game.
Typically, you either have inspiration or you don’t—you can’t stockpile multiple “inspirations” for later use. However, some campaigns make exceptions to this rule.
If you have inspiration, you can expend it after you make an attack roll, saving throw, or ability check in order to reroll the d20. You only reroll one dice, even if you rolled multiple, such as with advantage or disadvantage, and you can not use multiple inspiration points on one roll, even if you are allowed to stockpile multiple inspirations.