JOEL - The quick answer to this question is that a revelation was given to our prophet Joseph Smith which fixes the day of weekly worship on Sunday, the first day of the week (see D&C 59:9-12)
In Genesis we learn that God rested on the seventh day and that we should do likewise(Ex 20: 10-11).
However, Jesus' fulfillment of the Law of Moses brought several changes, including the practice of meeting on the first day of the week instead of the seventh. Evidence of this is suggested by certain events of Christ's postmortal ministry. For instance, it was on the first day of the week (Sunday) that he initially appeared to the apostles (John 20:19). It was also on the first day of the week that he reappeared to these same apostles (John 20:26). After Jesus' resurrection, it was on the day of Pentecost, a festival on the first day of the week (Lev. 23:15-16), that the assembled Saints and others received their most essential guide to eternal life, the Holy Ghost (Acts 2:1-12).
The early Christians understood the significance of this change in the day of their worship, as can be seen by their continued practice of congregating on the first day of the week:
"And upon the first day of the week, when the disciples came together to break bread, Paul preached unto them" (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)
If you think about it our earthly calendar really does not mean anything to God, whose measurement of time is completely different than ours. To members of the LDS Church the act of worshiping and receiving spiritual edification is more important than what day of the week it happens on. For example, in Middle Eastern countries the LDS day of worship is designated according to local religious tradition: Friday in Muslim countries and Saturday in Israel.
As Jesus said;
"The Sabbath was made for man, and not man for the Sabbath. (Mark 2:25).