Mitzvah #32, in the “Ten Commandments,” is a negative mitzvah: the prohibition against performing acts of creative labor on the Sabbath. This mitzvah is a positive one: the obligation to rest on Shabbos. Shabbos is so important that its observance is both a positive and a negative mitzvah. (The Sefer HaChinuch points out that Shabbos is so important that the Torah restates our obligation to observe it a full dozen times!)
As we mentioned in Mitzvah #32, to rest on Shabbos does not necessarily mean what people mean in English conversation by “to rest.” It means to refrain from acts of labor. Driving appears more “restful” than walking in the English, conversational sense, but walking is actually “restful” in that driving necessitates forbidden forms of labor.
Nevertheless, it is also important for us to “rest” in the more conventional sense, as well. In the Book of Isaiah, chapter 58, the prophet tells us, “If you restrain your steps because of Shabbos and refrain from doing your own business on My holy day, if you consider Shabbos a delight and honor God’s holy day by not going about your daily business, conducting your usual affairs or discussing mundane matters, then you will delight in God…” (13-14). These verses define some forms that our “rest” takes on Shabbos. We don’t run (except to shul or to perform a mitzvah), we don’t do things that are not “Shabbosdik” (like preparing on Shabbos for after Shabbos) and we don’t discuss matters not appropriate for Shabbos, such as business. (These principles are respectively known as hiluchecha, cheftzecha and dabeir davar; they are referenced in the Shabbos zemiros in the song Mah Yedidus.)
The obligation to rest on Shabbos is incumbent upon both men and women in all times and places. It is the subject of pretty much the entire Talmudic tractate of Shabbos, but starting heavily on 51b. It is codified in the Shulchan Aruch specifically in Orach Chaim 246 and 305. It is #154 of the 248 positive mitzvos in the Rambam’s Sefer HaMitzvos and #20 of the 77 positive mitzvos that can be fulfilled today as listed in the Chofetz Chaim’s Sefer HaMitzvos HaKatzar.