Cases: nominative

We introduce people and things by naming them:
     This is Dikaiopolis ὅδε ἐστίν ὁ Δικαιόπολις.
This is Paul. ὅδε ἐστίν ὁ Παῦλος
This is the (=his) house.     ὅδε ἐστίν ὁ οἶκος.
This is the name-case called nominative. The name comes from Latin, nominare = to name, hence to nominate someone, a nomination etc.

We use the nominative case form to name people as being (big, small, farmers, called X) or doing (running, sleeping, catching thieves etc). This doer of things is also called the subject of the sentence.

ὁ Δικαιόπολις αὐτουργός ἐστιν.
ὁ αὐτουργός ἰσχυρός ἐστιν.
ὁ ἄοκνος ἄνθρωπος πονεῖ
ὁ οἶκος καλός ἐστιν.

The form we are given in dictionaries when looking up a noun, pronoun or adjective is the nominative form, obviously, since it introduces the new word by name.