Once per adventure, you can declare that you are using inspiration to reroll an ability check. To use inspiration, you must simply describe how you were inspired by another player character. Then you can pick up the die and roll it again. Remember that you must use the new result (and no check may ever be rerolled more than once). After you use inspiration, you cannot use it again until you take a week-long rest.
It is up to you to decide what is inspiring for your character. However, the following conditions apply:
You should always use inspiration to recognize another player’s role-playing. That is, your source of inspiration should be another players' acting and descriptions, or the choices they made which reflect their character's personality, psychology, or moral fibre.
Inspiration may never be based solely on a die roll or mechanical effect. For example, you cannot gain inspiration from the time someone scored a critical hit.
Inspiration must be based on something that happened during the same adventure (not during a previous adventure).
The same thing cannot be used as a source of inspiration more than once. Likewise, you cannot take inspiration from something that has already been used as a source of inspiration by another player.
Some examples of valid sources of inspiration include:
A character's charming naïveté, which makes you want to protect them
A character's courage in the face of near-certain death
A meaningful conversation you had with another character about their background
A song the bard sang that raised your spirits
A difficult moral choice that a character made
A character taking a risk to help someone or something in need
A character's stolid devotion to their god, or to their personal principles
The unique way a character does things (that is, the player's evocative description of the character's actions)