Once you've appreciated something, you've seen what it is and what it means. If you think that wrestling alligators is a fun hobby, you haven't fully appreciated how dangerous it is.
The root of the adjective appreciated is the Latin appretiat-, meaning “to set at a price.” So if you have appreciated a situation, you have sized it up and you know the score. Until the crash, you dismissed bicycle helmets as unnecessary; that was before you appreciated their benefits.
