You experience guilt when you feel bad about doing something wrong or committing some offense. Guilt is also the state of having committed the offense — it's the opposite of "innocence."
The noun guilt stems from the Old English word gylt, meaning "crime, sin, fault, or fine." Feelings of guilt are typical after you've done something you shouldn't have, like cheating on your spelling test or stealing from your little brother's piggy bank. We often say that our conscience is the source of this feeling. If you're the prosecuting attorney in a criminal trial, your job is to prove the guilt of the defendant, that is, to prove that they committed the crime you're accusing them of.