The rest comes as the consequence of ceasing. That is what we are almost embarrassed to do as if it was a mark of weakness. To call to remember is for those Israelites to remember that they had once been slaves, and now were released and free to serve God. By inference - for us it means to remember what Jesus has done for us. I think that is best expressed in worship where we spend time remembering who we are and whose we are.
History Let's go back to history.
The Jews set apart the 7th day - we call it Saturday. Actually they counted their Sabbath from sundown on Friday to sundown on Saturday. They carefully established what they thought work was and prohibited it. By the time of Jesus there were numerous extra-biblical laws restricting the Sabbath. 39 different categories of work were prohibited on the Sabbath 1521 different tasks were isolated to avoid.