A more thorough explanation:

Definition: Liable to a fine; subject to having to pay a fine.

Example: If you park in a no-parking zone, you may be finable and have to pay a fine.

This means that if you break a law or a rule, you may have to pay a fine as a punishment. For example, if you get a speeding ticket, you are finable and have to pay a fine to the government. The word "finable" is used to describe something that can result in a fine.