The Sabbath was an important weekly reminder of God’s covenant with His people. After Moses went back to get a second copy of the commandments, it is the one that was now repeated to Israel:
35:2-3 You have six days each week for your ordinary work, but the seventh day must be a Sabbath day of complete rest, a holy day dedicated to the Lord. Anyone who works on that day must be put to death. You must not even light a fire in any of your homes on the Sabbath.
The ban on lighting fires shows how serious this was: the sixth day was a day of rest, even the women and servants were given a rest from cooking.
When the Sabbath was first mentioned, it was as an explanation to the Israelities when collecting their manna and quail: they collected twice as much on the sixth day, a day we would now call Friday, but they didn’t know why at the time. Moses had to explain:
Exodus 16:22-23 On the sixth day, they gathered twice as much as usual—four quarts for each person instead of two. Then all the leaders of the community came and asked Moses for an explanation. He told them, ‘This is what the Lord commanded: Tomorrow will be a day of complete rest, a holy Sabbath day set apart for the Lord. So bake or boil as much as you want today, and set aside what is left for tomorrow.’
The instruction to keep the Sabbath was then repeated as part of the ten commandments:
Exodus 20:8-10 Remember to observe the Sabbath day by keeping it holy.You have six days each week for your ordinary work, but the seventh day is a Sabbath day of rest dedicated to the Lord your God.
… with more detail given in Exodus 31:13–17. These scriptures explain the reasoning:
Exodus 13:13,16 … the Sabbath is a sign of the covenant between me and you from generation to generation. It is given so you may know that I am the Lord, who makes you holy. … 16 The people of Israel must keep the Sabbath day by observing it from generation to generation. This is a covenant obligation for all time.