Dative

The dative case denotes an indirect object (translated as "to ..." or "for ..."); means or agency, especially impersonal means (translated as "by ..."); or a location. It is also frequently used as an object of a preposition, and often, a preposition can take a noun in either the genitive or dative case with different meanings.

Examples

Εὐχαριστοῦμέν σοι Κύριε ὁ Θεός ὁ Παντοκράτωρ
We give thanks to you Lord God Almighty

You is dative here because it is the indirect object of the verb "give thanks".
Ἐν ἀρχῇ ἦν ὁ Λόγος
In the beginning was the word.

The beginning is dative here because it is the object of the preposition "in".