It's a little pot with a lid. You rub the inside with butter or oil then pop in your egg with some extras (seasoning, fetta, tomato, sausage etc) then screw on the lid and put it in a shallow dish of boiling water.

My Mum used to make them for us and they were really yummy.

ETA - There's an egg coddler appreciation society?! I'm there they sound like my kind of people.