In civil law, recourse means that a person liable to pay compensation for damages (e.g. an insurance company) falls back on a third party (e.g. person causing a damage) who is liable vis-à-vis the former.
 

Examples: A third-party liability insurer is liable for the payment of damages and demands re-payment from the person causing the damage. 
A fire insurance provider pays a compensation to the owner of a building who sustained damage and takes recourse on the person causing the fire.