Just as the church substituted Israel as the people of God, its day of observance also changed. The sabbath was part of the law of the old covenant (see Exodus 20). The first day is the celebration of the new covenant. In Israel, the sabbath was a day of individual rest. In the church, the first day is for meeting together.
The first day is the day of the Lord because Jesus was raised on this day (Matthew 28.1). On this day he appeared to the disciples (John 20.19, 26). So the church met on the first day.
Paul tells the Corinthian church to make an offering on the first day, as he had told the Galatian churches, because they all were already meeting regularly on that day (1 Corinthians 16.2). It was the practice among the churches. The phrase in this verse has the meaning of “the first day of every week” (ESV, NASB, NIV) or “on every first day of the week” (YLT). Paul urges a regular offering to be done, since they are already meeting every Sunday.
The “breaking of bread,” which in the New Testament often refers to the spiritual act of remembering Christ in a meal, is also called the “table of the Lord” (1 Corinthians 10.21) and the “Lord’s supper” (1 Corinthians 11.20).
John calls the first day “the Lord’s day” (Revelation 1.10). Evidently, by the time he wrote, this phrase was common among the saints so that there was no need to explain which day it was. The only day which would qualify for a well known day would be the first.
John uses the phrase without explanation, even though it was used in the Old Testament to refer to a great and terrible day of judgment or redemption (cf. Joel 1.15; 2.1). The New Testament also uses it to refer to the final day of judgment when Christ will return a second time (1 Corinthians 1.8; 5.5; 2 Corinthians 1.14; 1 Thessalonians 5.2; 2 Thessalonians 2.2; 2 Peter 3.10). But for John it refers to a day he was then living in a special way and no doubt in worship to God.
The connection between the day of the Lord and the table of the Lord becomes especially clear in Acts 20. Paul was in a hurry to get to Jerusalem by Pentecost. So much so that, as he neared Ephesus, he called for the elders to come to him, rather than taking out the extra time to go to the city to talk with them (vv. 16-17).
Shortly before that, however, he delays in Troas for all of seven days (v. 6). Why does he stay there for so long? Apparently, because he arrives there on a Monday and desires to meet with that church on a Sunday. With the Jews’ counting parts of a day as a day, Luke would possibly have counted Monday as a day, making it seven days until Sunday.
Why the need to wait for so long? Because it was only on Sunday that the church ate the Lord’s supper: “On the first day of the week, when we met to break bread, Paul began to speak to the people, …” (20.7 NET; see also ERV, NLT). Luke states that this was their purpose for meeting on the first day: “the church met on the first day of the week for the purpose of breaking bread” (Edwards 552). Breaking bread in this verse is an “obvious reference to the Lord’s Supper” (ibid.; pace CEB).
So, together with the other references, Acts 20.7 ties together the first day of the week, which is the Lord’s day, and the table/supper of the Lord.
Any day of the week is a good day to meet with the saints. The first day of the week is the Lord’s day in a special way because the church meets around his table.
Edwards, W.T. (1990) “Lord’s Day,” in Mercer Dictionary of the Bible, Watson E. Mills, gen. ed. (Macon, GA: Mercer University Press): 522-23.
Update: The author failed to check his Greek text: The preposition eis is not found in Acts 20.7. The reference has been removed. The point still stands, however, that the verse does express the purpose for which they met, to eat the Lord’s supper.