Dative is a grammatical case for a noun. Dative marks, generally, the indirect object of a verb. Dative cases are found in Latin, Old English, and German among other languages. Compare nominative case, accusative case, ergative case, genitive case, vocative case, ablative case.
While dative case is no longer a part of the English grammar, it survives in a few set expressions. One good example is the word methinks, with the meaning "it seems to me". It survives in this fixed form from the days of Old English (having undergone, however, phonetical changes with the rest of the language), in which it was constructed as me (the dative case of the personal pronoun) + thinks ("to seem", a verb closely related to the verb "to think", but distinct from it in Old English; later it merged with "to think" and lost this meaning).
The dative can occur in English without a preposition ('to' or 'for') as in "He gave me that" or "He built me a snowman". In both examples the "me" is dative.