The phrase often relates to a physical feeling, like being sick, as a reaction to smells or sights. Seeing the spoiled food turn your stomach, making it hard to stay in the room.
Pro Tip 2/3
Extreme Disgust
It emphasizes a strong level of disgust, more than just finding something unpleasant. The thought of eating insects might turn your stomach.
Pro Tip 3/3
Colloquial Use
Used in informal contexts, you might not find this phrase in formal writings or speeches. He skipped the gory scene because it tends to turn his stomach.