From latris (a hired menial); to minister (to God), i.e. Render religious homage -- serve, do the service, worship(-per).
b. universally, to serve, minister to, either gods or men, and used alike of slaves and of freemen; in the N. T. to render religious service or homage, to worship (Hebrew עָבַד, Deuteronomy 6:13; Deuteronomy 10:12; Joshua 24:15); in a broad sense, λατρεύειν Θεῷ: Matthew 4:10 and Luke 4:8, (after Deuteronomy 6:13); Acts 7:7; Acts 24:14; Acts 27:23; Hebrews 9:14; Revelation 7:15; Revelation 22:3; of the worship of idols, Acts 7:42; Romans 1:25 (Exodus 20:5; Exodus 23:24; Ezekiel 20:32). Phrases relating to the manner of worshipping are these: Θεῷ (so R G) λατρεύειν πενυματι (dative of instrumentality), with the spirit or soul, Philippians 3:3, but L T Tr WH have correctly restored πενυαμτι Θεοῦ, i. e. prompted by, filled with, the Spirit of God, so that the dative of the person (τῷ Θεῷ) is suppressed; ἐν τῷ πνεύματι μου ἐν τῷ εὐαγγελίῳ, in my spirit in delivering the glad tidings, Romans 1:9; τῷ Θεῷ ἐν καθαρά συνειδήσει, 2 Timothy 1:3; μετά αἰδοῦς καί εὐλαβείας or (so L T Tr WH) μετά εὐλαβείας καί δέους, Hebrews 12:28; ἐν ὁσιότητι καί δικαιοσύνη, Luke 1:74; (without the dative Θεῷ) νηστείαις καί δεήσεσι, Luke 2:37; λατρεύειν, absolutely, to worship God (cf. Winer's Grammar, 593 (552)), Acts 26:7. in the strict sense; "to perform sacred services, to offer gifts, to worship God in the observance of the rites instituted for his worship": absolutely, Hebrews 9:9; Hebrews 10:2; specifically, of the priests, to officiate, to discharge the sacred office: with a dative of the sacred thing to which the service is rendered, Hebrews 8:5; Hebrews 13:10. (Euripides, others.)