to give thanks: to express gratitude, most often to God
This is the ordinary New Testament word for giving thanks. In the wide majority of its uses the gratitude is directed to God: in prayer, in worship, and as the settled posture Paul urges on believers (give thanks in everything). The word names the act of voicing that gratitude, not merely feeling it.
The same word does double duty for two narrower settings that grow out of that core. One is the blessing said over food: when Jesus took bread or the cup and gave thanks, this is the verb, and it became the standard term for the prayer of grace before a meal. The other is plain human gratitude, thanking a person for what they have done, which the word can carry just as naturally as thanking God.
Because the noun built from it, often written in English as Eucharist, came to name the Lord's Supper, readers sometimes hear a sacred technical term where the writer simply meant to give thanks. The verb itself stays general: it is the everyday act of thanksgiving, whoever the thanks are owed to.