Every sentence has a subject. This is the thing – be it person, animal or inanimate object (I’m looking at you, lamp) that does the action in the sentence. For example:
Der Hund springt aus dem Hundebett.
Here, the dog is doing the jumping, and so it is the subject. Aaaand, because it’s the subject, it is in the Nominative Case. The Nominative is just the case we use for the subject of the sentence.
Here are the definite and indefinite articles in the nominative:
The declensions of the indefinite article
One extra thing to remember with the nominative case is that there are certain situations where you might have to put your object (which would usually be in the accusative) in the nominative also. This happens when you are using verbs like:
sein – to be
werden – to become
bleiben – to remain
heißen – to be called
scheinen – to seem
These are all verbs which refer to the state of existence of the subject, and they function as a kind of grammatical equals sign:
Ich bin Schauspieler. -> Ich = Schauspieler.
Ich bleibe eine arme Frau. -> Ich = eine arme Frau.
The nouns on each side of the equals sign are on equal grammatical footing, and so they both take the nominative case.