Mussakka is essentially just a stew from seasonal vegetables with a tomato base and chick peas or beef for protein. More often with meat in Istanbul, and vegetarian in the Aegean region.
There is a long discussion concerning the origin or the dish, being either Turkish of Greek. I find this argument ridiculous and of no apparent value whatsoever. The food is delicious let us share it across the world.
Additionaly, Mussakka is often confused with İmam bayıldı which is an eggplant stuffed with vegetables broiled in a tomato sauce, or its variation Karnıyarık which is essentially the same but with meat inside.