When the drunk driver is charged with DUI and that case is prosecuted through the state attorney's office, the judge gives the victim an opportunity to show evidence that they have had out-of-pocket expenses. If there is clear evidence the judge would then order the drunk driver to pay those out-of-pocket expenses to the victim. This is what you call a restitution order.
The conviction of a DUI and the order of the court to make restitution to the victim under Florida law prevents the drunk driver from denying that they were driving under the influence. This is why it is important to pursue the restitution order even if the drunk driver can't pay it because it will strengthen the victim's case.