The Lord’s Day in this context, is Sunday rather than the Sabbath, which was previously observed on Saturday’s (Exodus 20:8-11). God gives the commandment to establish Saturday as the day of rest, however, in the New Testament, the church and all the people rested and began to worship on the first day of the week, which is Sunday.
In (Exodus 20:8-11) the basis for the commandment was that God rested on the seventh day, after his six days of work in creation. God then blessed the seventh day and sanctified it. Jesus corrected the distorted view of the Pharisees by saying, “The Sabbath was made for man, not man for the Sabbath” Mark 2:27-28
The Sabbath was not instituted to enslave man, but to benefit him. In (Colossians 2:16-17) the substance of the Sabbath is what Christ represents. The Sabbath was a type and shadow of things to come in Christ. The observance of the Sabbath was associated with redemption. Moses talked about keeping the Sabbath day (Deuteronomy 5:15), which was a type and shadow of redemption that would come through Christ. It symbolizes rest from work and the rest provided by Christ’s finished work in the salvation of man.
The command establishing Saturday as a day of rest and worship is the only commandment not repeated in scripture from the Old Testament into the New Testament. The New Covenant or New Testament believers, are “NOT” under the Law or Old Covenant Testament Laws (Romans 6:14; Galatians 3:24-25).
Christ was resurrected on the first day of the week, Sunday (Matthew 28:1). Jesus continued to make appearances to people after his resurrection on succeedingSundays.
“Then the same day at evening, being the first day of the week, when the doors were shut where the disciples were assembled for fear of the Jews, came Jesus and stood in the midst, and saith unto them, Peace be unto you, And after eight days again his disciples were within, and Thomas with them: then came Jesus, the doors being shut, and stood in the midst, and said, Peace be unto you.” John 20:19 & 26
The decent of the Holy Spirit at Pentecost was on a Sunday (Acts 2:1).
The early church was given this new pattern of Sunday worship; “And upon the first day of the week, when the disciples came together to break bread, Paul preached unto them, ready to depart on the morrow; and continued his speech until midnight.” Acts 20:7
Upon the first day of the week let every one of you lay by him in store, as God hath prospered him, that there be no gatherings when I come. 1 Corinthians 16:2
“I was in the Spirit on the Lord's day, and heard behind me a great voice, as of a trumpet” Revelation 1:10
The appearance of Jesus to John on the island of Patmos was also on a Sunday which is referred to as the Lord’s Day, is Christ Day, because He established it as such from the time of his resurrection, which again was on a Sunday.
For these reasons, for over 2000 years and starting from the time at Pentecost, Christians began to observe Sunday rather than the Jewish Orthodox Sabbath of Saturday, all over the World.