1. To face the repercussion of being incorrect after one's claim, boast, or assertion is refuted; to eat one's words. The member of parliament will have to eat his shirt for his claim that no new taxes would be introduced this year. You'll be eating your shirt if this new engine isn't as fast as you say it is.

2. To take a loss on a wasted or unfruitful investment. I ended up having to eat my shirt on the cost of the lumber for the new shed after it was ruined by the rain.