Feral cats tend to stick to specific areas, and may form loose colonies with other local feral cats. These colonies can range in size from a handful to dozens of adult cats, and, in the absence of concerted spay and release efforts, the size of the colonies tend to continue growing.
Larger populations of feral cats in neighborhoods can become a real nuisance, with issues including noise (particularly when one or more females go into heat), food raids (garbage cans being tipped over, unguarded food snatched, etc.), and waste (gardens make good substitute litter boxes).
When local cats are viewed as pests and nuisances, the likelihood of abuse from the human residents increase. These cats are at risk of deliberate poisoning, getting shot, trapped in inhumane ways, or even torture.
The idea behind spay and release is that you are allowing the animals to live out their lives in a way that gives them at least some chance of happiness, while putting a stop to the cycle of breeding to avoid more cats being born into the rather harsh conditions most feral cats put up with. The gradual reduction in numbers reduces the pressure from the local environment on these animals, largely by making them less of a nuisance.
People actively involved in spay and release programs frequently feed the feral cats in their neighborhood. Their houses or businesses therefore tend to be areas where the local feral cat population will converge. This makes it easier to keep track of which cats they've already captured and had "fixed", so if one is accidentally recaptured, they simply release it immediately instead of bringing it to the vet (unless they decide to bring the cat in for other medical reasons).
If a cat that has already been fixed is captured/recaptured, a veterinarian will be able to ascertain this prior to committing to surgery.
As thkala mentioned, there are issues with finding homes for feral cats. Simply put, they tend to make horrible pets.
My mother was active in spay and release with the local cats in her previous neighborhood, and the people who owned the house prior to her made a habit of feeding the neighborhood cats. Over time, all but one of the local cats disappeared (presumably dead). When she finally moved to a new house, she caught the remaining feral cat, and brought it with her (fearing that it had become overly dependent upon her providing food, which was not something she could guarantee the next owners of the house would continue).
She still has this cat. It lives in her basement, and hides in a storage area. It does come out to interact with the domesticated cat they also have, but my mother almost never sees her (and when she does, it is just a quick glimpse as the cat runs and hides).
Very few people want an animal like that living in their house, and therefore finding a home for individual animals, let alone an entire colony, is almost impossible.
Many areas have charitable organizations dedicated to supporting the costs and logistics of spay and release programs. These programs may offer live animal traps, assistance in finding local veterinary offices that will assist with spaying, or even vouchers to get the procedures done at a reduced cost. Individual veterinary offices may also support the practice with discounted rates or other services.
It is worth a quick search in your area to see if there are any spay and release organizations nearby.