Meaning of the Lord's Day
The following are quotes taken from: Messages For Building Up New Believers (1), The Collected Works of Watchman Nee, Set Three, Volume 48, Living Stream Ministry, 272 pages.

Everything in the Old Testament is a shadow of the coming good things (Heb. 10:1).  Like all other types in the Old Testament, the Sabbath which God gave man has its spiritual significance.  God created man on the sixth day and rested on the seventh day.  As soon as man was created, he rested on the seventh day.  As soon as man was created, he did not enter into work but into God's rest.
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Hebrews 10:1

God worked six days and then rested one day.  But when man came, there were not six days followed by one day but one day followed by six days.  Man rested first and then worked.  This is the principle of the gospel.  The Sabbath is a type of the gospel.  Salvation comes first; work comes later. First we have life; then we have the walk.  Rest comes before the work and the walk.  This is the gospel.  God shows us that He has already prepared the rest of redemption.  After we enter into it, we work.  
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The significance of the Sabbath is that man stops his work and enters into God's rest.  For man to enter God's rest means that man does not do his own work but instead accepts God's work.  Therefore, it is a great sin to break the Sabbath.  If you work when God asks you not to work, you have rejected God's rest.
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Originally, the Sabbath was a day of physical rest, but in the New Testament it becomes a day of spiritual pursuit.  This is an improvement from the Old Testament.
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Concerning the Sabbath, the Scripture said, “God blessed the seventh day” (Gen. 2:3), but the Scripture calls the day the Lord Jesus resurrected from the dead “the first day of the week” (Matt. 28:1).  It does not say that the Lord Jesus resurrected on the seventh day but that He resurrected on the fist day of the week.  All the Gospels show us that the Lord Jesus resurrected on the first day of the week.  This shows that God is turning our attention to the first day of the week.
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Genesis 2:3; Matthew 18:1

The Lord's Day is totally different from the Sabbath of the Old Testament.  On the Old Testament Sabbath day, one could not do this or that; everything was negative.  If a man broke the Sabbath, he would be put to death.  This is a very heavy punishment.  But we do not have this stigma today.  God prophesied that He would choose another day in the New Testament age.  God did not say what could or could not be done on that day.  Rather, He told us what should be done.  God wants us to exult and rejoice on that day.
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The things of the old creation stopped on the last day of the week, the seventh day.  The new creation began on the first day of another week.  Consequently, the new creation has been clearly separated from the old creation.
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God purposely picks one day out of seven and calls it by a special name.  Revelation 1:10 calls it the Lord's Day.  The writings of the early church fathers give us ample proof that “the Lord's Day” refers to the first day of the week.  This is also the day for the church to meet.  There are many examples in the writings of the early church fathers which prove that the meetings were always held on the first day of the week.  This was true from the time of the disciples of John until the fourth century.
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Acts 20:7 says, “And on the first day of the week, when we gathered together to break bread…”  According to the original text, the first day of the week here does not refer to the first day of a certain particular week.  It means that they met to break bread on the first day of every week.  At that time all the churches spontaneously gathered together to break bread in remembrance of the Lord on the first day of the week.
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Acts 20:7

The breaking of bread signifies two things in the Bible:  the remembrance of the Lord and the declaration of our fellowship with all the children of God.
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1 Corinthians 16:1-2 says, “Now concerning the collection for the saints, just as I directed the churches of Galatia, so you also do.  On the first day of the week each one of you should lay aside in store to himself whatever he may have been prospered, that no collections be made when I come.”  On the first day of every week, every one should offer to the Lord according to his income.  This is a good practice.  The more a person receives from the Lord, the more he should give.
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1 Corinthians 16:1-2