I think it is pretty simple.
The Jewish Sabbath is Saturday and that is very clear and we still believe this to be true. We actually don’t celebrate the jewish sabbath anymore we actually celebrate the 8th day or the day of the new creation. It is actually some very beautiful theology that goes behind this.
We celebrate the sabbath on Sunday’s now for a very simple reason. Christ rose from the dead on Sunday so we celebrate the Lord’s resurrection for our sabbath. Think about it this way. In Genesis God spend 6 days working in his creation to bring about man and everything else and rested on the 7th day. The Church tells us that Christ was crucified on Friday the 6th day. (The 6th day may be a type of the passion of Christ but I’m not sure) Than Christ rests on the 7th day in the tomb. Than on that glorious 8th day Christ brings about a new creation.
to put it simply
Christ died on day 6
rested on day 7
brought in the new creation on day 1 (or as the Church says day 8)
So because we follow Christ we remember the day of his new creation, the 8th day.
1166 “By a tradition handed down from the apostles which took its origin from the very day of Christ’s Resurrection, the Church celebrates the Paschal mystery every seventh day, which day is appropriately called the Lord’s Day or Sunday.” The day of Christ’s Resurrection is both the first day of the week, the memorial of the first day of creation, and the “eighth day,” on which Christ after his “rest” on the great sabbath inaugurates the “day that the Lord has made,” the “day that knows no evening.”37 The Lord’s Supper is its center, for there the whole community of the faithful encounters the risen Lord who invites them to his banquet: (1343)
The Lord’s day, the day of Resurrection, the day of Christians, is our day. It is called the Lord’s day because on it the Lord rose victorious to the Father. If pagans call it the “day of the sun,” we willingly agree, for today the light of the world is raised, today is revealed the sun of justice with healing in his rays.
1167 Sunday is the pre-eminent day for the liturgical assembly, when the faithful gather “to listen to the word of God and take part in the Eucharist, thus calling to mind the Passion, Resurrection, and glory of the Lord Jesus, and giving thanks to God who ‘has begotten them again, by the resurrection of Jesus Christ from the dead’ unto a living hope”:
When we ponder, O Christ, the marvels accomplished on this day, the Sunday of your holy resurrection, we say: “Blessed is Sunday, for on it began creation … the world’s salvation … the renewal of the human race.… On Sunday heaven and earth rejoiced and the whole universe was filled with light. Blessed is Sunday, for on it were opened the gates of paradise so that Adam and all the exiles might enter it without fear.
From the CCC