What is the meaning of Matthew 28:19-20?

19 Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost: 20 Teaching them to observe all things whatsoever I have commanded you: and, lo, I am with you alway, even unto the end of the world. Amen. (Matthew 28:19-20 KJV)

Annotated Bible Notes

Go ye. This command, being given to the assembled multitude of disciples, shows that it is the duty and the privilege of every true disciple to endeavor to ‘make disciples of’ others see Ac 8:4

teach. Or, ‘make disciples of’ (R.V); teach them the doctrine concerning me, and endeavor to lead them to receive it. We have here the threefold object of the preachers of the Gospel—to make men disciples of Christ, by converting them to the faith; to bring them to a public profession of the faith, by baptism; and to train them up in the practice of universal holiness.

All (the) nations. Not confining your labor; to your own countrymen. Yet it required another express revelation Ac 10:1-48 to teach the disciples that the gospel tidings were not to be confined to the Jews, or to the proselytes, in ‘all the nations,’ but to be preached to all men.

baptizing them. All who are made disciples are to be baptized. Baptism is the solemn rite of admission into the visible church, and is designed as a profession of faith in the character and the word of God, as revealed in Holy Scriptures.

in the name. Rather, ‘into the name,’ etc. (R.V.); a formula implying union with and dedication to. And it should be observed that it is not into the names, but into the name; showing that, with a distinct recognition of the different parts which the Father, the Son, and the Holy Spirit take in the great work of salvation, there is joined an equally distinct apprehension of the unity of the Godhead, as the fountain of authority and the source of blessing: compare 2Co 13:14 In the Acts, the recorded instances of baptism are in the name of Jesus only, but the gift of the Holy Spirit is associated with the ordinance: in promise Ac 2:38 preceding the rite Ac 10:44; Ac 10:47 or following it Ac 8:17; Ac 19:6

I am with you alway (‘all the days ‘). The presence and power of Christ are necessary to success in His service. And they are promised, as an all-sufficient strength and comfort, to His faithful servants, in all their Christian labor, ‘unto the end of the world,’ or, as R.V. marg., ‘the consummation of the age,’ the accomplishment of all the great purpose; which mark and crown the era of redemption.