The nominative case is another way of describing the function of the subject, predicate nouns, and predicate adjectives. The subject is the “doer” or performer of the verb in a sentence. Predicate nouns rename the subject(s) and are often pronouns or names. Consider the following sentence:
The girl is tall. Her name is Gretchen.
In the above example, the second sentence consists of a subject (“Her name”) and a predicate noun (“Gretchen”); both are referring to the same noun (i.e. name), and can be thought of as follows: her name = Gretchen. Regardless of position, the sentence will mean the same thing: Gretchen is her name = Her name is Gretchen.
The predicate adjective (first sentence in the example above) is an adjective that describes the subject, and is typically on the other side of the verb “to be.” In the example, this is the first sentence: The girl is tall. “Tall” describes “the girl,” and is not declined — that is, there is no ending affixed to the adjective.