The FAA conducts random in-person inspections of aircraft and pilots. These inspections are commonly referred to as "ramp-checks." During the ramp check, the inspector will ask for aircraft documentation, as well as pilot documents. These include pilot certificate, and medical.
There is an old, but persistent myth that a pilot must physically hold the pilot certificate and not allow the inspector to hold it, because it could be considered "surrendering" the certificate. This is idiotic, but I still hear pilots perpetuate the falsehood to this day.
Surrender is a formal process of not only giving the medical or pilot certificate back to the FAA, but formally declaring that one is surrendering the certificate. If the FAA wants to take it, they may do so through suspension or revocation, but neither of those are accomplished by simply holding the certificate, and the FAA is not allowed to take either one without administrative action (a suspension or revocation).
If one surrenders the medical, it may be at the FAA's direction, or one may choose to do so. Just as one may surrender one's driving privileges (as opposed to simply laying the driver license on the bureau and never using it again), one may surrender a pilot certificate or medical certificate.
Tired Soul gave the example of one who surrenders certification in an attempt to forestall FAA enforcement action. That may or may not work, but it's about the only reason I could imagine one surrendering either the pilot certificate or medical.
It might be a way of putting closure on one's flying; one might have a medical issue that has eliminated one's chance to fly again (deteriorating eyesight or another condition which makes flying impractical or impossible): one might surrender the certificate as a way of hanging up one's spurs. Otherwise, I see no value in giving up what one has worked so hard to get; I would choose to let it simply expire.