One-hundred percent humidity means the air is completely saturated and is holding its maximum amount of water vapor. That will make it appear foggy outside with perhaps some drizzle or mist.
But the air doesn't have to be fully saturated to have rainfall. When it's raining, it just means the raindrops have become heavy enough to where they're heavier than the surrounding air, but that doesn't mean the air has to be completely saturated. A majority of the time when it's raining, the humidity is less than 100 percent -- likely between 60 and 100 percent.