"Debajo de..." is relative. Thigs are "debajo de" other things. It can be translated by "under...". It is what we call a "locución prepositiva" and it works just like a preposition:
"The ball is under the table" = "La pelota está debajo de la mesa".
Sometimes, we use "debajo" as an adverb. In this case, it can be translated by "under it" in English:
"Do you see that table? The ball is under it." = "¿Ves esa mesa? La pelota está debajo."
"Abajo" is an adverb. It means "the place below" or "the lowest part".
In a house or building, it will ususally mean "downstairs". "La cocina está abajo" = "the kitchen is downstairs".
If you are in a high place, like a mountain, hill, etc., you will say of things/people who are at ground level that they "están abajo".
It can also mean a direction: "down". "The elevator is moving down" = "Es ascensor se está moviendo hacia abajo".
Sometimes, you may see "abajo de" instead "debajo de". It is less common, but correct. The other uses of "abajo" and "debajo" are distinct, though.
There's also the preposition "bajo". It's used like "debajo de" and it means the same:
"La pelota está debajo de la mesa" = "La pelota está bajo la mesa"
The adjective "bajo" means "short", but that's not related to your question.