To be yellow-bellied is to be cowardly or easily scared. If you're yellow-bellied, you're not brave. It’s the kind of word cowboys use, partner.
This word originally applied to birds that literally have a yellow belly, like the yellow-bellied sapsucker. From there, it came to mean an insult for cowards. If you're afraid to ask someone on a date, you're yellow-bellied. If you're easily frightened or spooked, you're yellow-bellied. This is often used as an insult or challenge, like "What are you, yellow-bellied?!"