Similar to eating spicy food, there are a lot of old wives’ tales about eating eggplant to induce labor. But there’s no scientific evidence that back them up. No studies have been done (yet) to determine whether or not eggplant has any effect on the labor process, so any “evidence” is purely anecdotal.
You may have heard of someone who ate eggplant and then went into labor, but this was likely someone who was already 40 weeks or beyond and feeling desperate. Their body was likely already primed for labor and the process started on its own. Remember that correlation doesn’t equal causation.
Eggplant itself is safe to eat while you’re pregnant, but you might want to stay away from eggplant parmesan right before labor—it likely won’t induce you, but it very likely will give you some nasty heartburn.