Every sentence in this lesson puts the noun in the nominative case — either as the subject of the sentence or as a predicate noun after sein ("to be"). The indefinite article changes depending on the noun's gender:

Masculine and neuter share the same nominative article, ein — only the feminine article changes, to eine. This is the base/dictionary form of the indefinite article, the one that then changes in the other cases (einen in the accusative, einem/einer in the dative, eines/einer in the genitive).