Each completed mission in Metal Gear Solid V can be repeated. This option becomes available after visiting the Mother Base for the first time (during mission 2 - Diamond Dogs). From that moment, while using the helicopter, you can select from the mission list not only new missions, but the ones already completed as well.
Repeating the missions allows you to test other paths to mission objectives or complete some requirements in different ways. The main motivation to mission repeating should be obtaining higher rank. When completing a mission for the first time, it might be difficult to obtain S rank due to the lack of proper equipment or simply not knowing the territory and mission targets. In addition, mission repeating is a good way for earning GMP and for taking care of excluding mission objectives and hidden targets, about which you didn't know when completing the mission for the first time.
Warning - If you are going to repeat a mission you will see that every quest you have already completed is still considered done. You don't have to complete them again although you may do it if you want to achieve a higher rank.