Greek islands generally have a lot of cats and Aegina is no exception. The port area has the highest concentration — they live under boats, in the narrow spaces between buildings, and in the open areas near the fish market where discarded scraps make for easy eating. Fishermen routinely feed them and several tavernas have semi-official resident cats who sit under tables with the faint hope of fallen fish.
Most of these animals are not wild in the sense of being unapproachable. They are used to people and will accept food or attention offered calmy. Approaching one abruptly or making loud noises is not recommended and will not end well. Children who want to interact with them should be supervised and taught to offer a hand for sniffing first.
There are local volunteer groups that run trap-neuter-return programs on the island, which is why many of the cats have clipped ears marking them as neutered. This keeps the population stable and reduces the number of sick or malnourished animals. If you intend to feed them, stick to appropriate foods and avoid anything with onions, garlic, or significant spicing.
If you are at a taverna and a cat approaches your table, the polite response is to not feed it from the table (this encourages more) but you may offer a small piece of plain fish or meat from your hand if you wish. Staff will generally not object to a moderate level of tableside cat attention as it happens all the time and many visitors seem to enjoy it as part of the experience.