An eggbound chicken (you can also have an eggbound duck) is when the egg is stuck inside and will not come out.
We had a very energetic chicken that suddenly became quiet, reserved, and stopped moving. I always count heads every night before we put our chickens and ducks away (they free range during the day), and I was missing one. I found her behind the bushes. She let me just walk up to her and pick her up. I have sweet chickens, but she is not one of the "sweeter" ones. She isn't mean, she just doesn't care for human companionship. Anyways, we set her down and she was waddling like a duck. So we looked up what to do on here.
You put the hen or duck in warm bath water for 45 minutes with epson salt and make sure that the egg maker, and where the egg comes out is under water. The warm bath helps them not strain so much. If it strains too much a prolapse can occur (where the organs flip outside of the chicken/duck). Luckily, that did not happen to us! We put epson salt and lavender in the water. Then we got a pair of gloves and inserted our finger into the vent to see if we could feel an egg. There was no egg, so I ran to the store and got some calcium tablets (calcium helps eggs pass) and polyvisol (multivitamin) and we force fed it to the chicken. Then we left her in a dark room over night to deactivate her egg maker. By the morning time, she had pushed that egg out. The egg was a soft shelled egg (where the egg is mushy instead of the hard coating), and that is why she was having such a hard time passing it. Sometimes though, it's a regular egg but is stuck. If it wasn't for the people and the advice we found on here, she might not have made it.