One of the main characteristics of those two domains is that all prokaryote are one cells organism, while the eukaryote and animals and plants are multicellular organism. We know that prokaryote is the older than all the organism which exist now in the world, that mean it was exist before animals and plants exist.
As prokaryote is one cell organism, to create new form of life, some of them merge together, for a better explanation one bacteria swallow another one.
When we consider the both, they got no more one, but two. When bacteria divided