The phrase often indicates a gut feeling that something bad is about to happen. As the dark clouds gathered, I had a sinking feeling about the trip.
Pro Tip 2/3
Not Literal
It's a metaphorical feeling, not a physical sinking. When she didn't answer her phone all night, I got that sinking feeling.
Pro Tip 3/3
Emotional Weight
The phrase carries an emotional weight and is often used during troubling or uncertain situations. Hearing the sirens in the distance, he felt a sinking feeling.