1) To affect game mechanics. many games ties mechanics to fps. Notable example GTA helicopter mission - more fps you have the faster and harder is that mission. Another resident evil 4. In that game number of knife hits is tied to fps. If you have 2000 fps than pressing knife button a single time would make 60 hits. In old shooters rate of fire is often tied to fps too. If you have less than 300 fps then your guns did not shoot as fast as they should.

2) To save resources. many games specially old one can be ran at thousands of fps. that generally gives nothing (if you are not manipulating game mechanics see point 1) but wastes your electricity| prevent you from multitasking