The difference between French vanilla and vanilla is in the process of making ice cream. The standard way of making the base for vanilla ice cream does not use eggs, while the French vanilla process is more of a custard-style that uses eggs in the base.
Vanilla comes from a orchid-like plant known as flat-leaved vanilla. The plant produces fruit, known as a pod, which has beans that are scraped out. The pods can be used intact, but more often, the pods are turned into a liquid extract and added to many different recipes, both sweet and savory, with frequent uses being baked goods and dairy-based desserts.