What it is
A fig is not really one fruit but a syconium: a soft, hollow pouch lined on the inside with dozens of tiny flowers, which is why botanists call it an infructescence rather than a berry. Whatever you call it, it grows on a tree and holds no animal tissue, so by the plain definition of veganism, avoiding animal products, a fig qualifies with no asterisk needed. The reason anyone hesitates is the fig wasp, and the biology really is worth knowing. In the wild, and in certain commercial varieties, a female wasp squeezes into an unripe fig through a pinhole opening called the ostiole, usually tearing off her own wings and antennae to fit, pollinates the flowers, lays her eggs, and dies inside the fruit. The plant then releases an enzyme, ficain, that breaks her body down, so what a person might eat is not a wasp but a fig that has absorbed one.
So are you eating wasps?
Here is the honest, calming version of the answer. The wasp-and-fig bargain only applies to figs that need pollinating, and a great many of the figs we actually eat do not. Common-type figs, which cover a lot of what you find fresh and dried, are parthenocarpic: their flowers are all female and they set fruit with no pollination, and so no wasp at all. Where a wasp is involved, in the Smyrna-type figs that must be pollinated by a wasp carrying pollen from a wild caprifig, the insect is minute, is broken down by the fruit's own enzymes, and what is left is measured in specks rather than bodies; and even then the thing on your plate is a plant, not an animal product. This is why figs are treated as vegan across the board: the definition turns on what a food is, not on every creature that touched it while it grew, and by that measure an apple visited by a bee and a fig pollinated by a wasp are both simply fruit.