The phrase usually implies that the person did something bad or unprofessional to deserve being fired. After the fiasco, she was out on her ear without a second chance.
Pro Tip 2/3
Sudden Removal
It suggests that the removal was quick and without hesitation, often unexpectedly for the person involved. Once the fraud was uncovered, he was out on his ear by lunchtime.
Pro Tip 3/3
Informal Context
It's an informal expression, so it's best used in casual conversation, not in formal writing or situations. Mess up like that again, and you'll be out on your ear, I guarantee it.