On Shabbat (the Sabbath Day) you should rest. This is because God ceased creating on the 7th day which is Shabbat. During Shabbat one can visit with family and friends, pray, study (no writing though), go for walks, and pretty much anything that doesn't fall within the 39 categories of "work" as specified in the Torah.
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There are two main aspects to Shabbat observance: what we do and what we don't do.
What we don't do: we're not permitted to work on the Shabbat (Exodus ch.20). This includes 39 categories of productive interaction with the world, such as planting, writing, kindling fire, etc. (Talmud, Shabbat 73b).
There's often a kiddush (refreshments) afterwards, and congregants then have a chance to schmooze (to talk). Towards the late afternoon, there's another (short) service (Shabbat mincha).
After Friday night services and on Shabbat morning after services, we come home, often with guests, make kiddush (blessing over wine), and have a leisurely multi-course Shabbat meal including singing and words of Torah. Customarily, that week's Torah-reading (parsha) will be a topic of conversation; and the children of the family will be asked to speak of what they've learned in school.
Husband and wife, in particular, finally have a chance to be together after a hectic week.
Sabbath is the resting day in a week. Judaism holds Sabbath on Saturday. They don't do anything on that day. Christianity changed Sabbath to Sunday to remember Jesus' resurrection, and that's why they have church services on Sunday.
The question answers itself: not keeping the Sabbath day holy is a sin.
The Sabbath occurs every week.
The Torah establishes the Sabbath with commandments to keep the Sabbath day, to remember the Sabbath day, and constraining what may be done on the Sabbath. And, in the Jewish liturgy that emerged from this framework, the Sabbath morning service includes a Torah reading where, traditionally, about 1/52 of the Torah is read, so that over the course of the year, every Jew who attends Sabbath services on a regular basis will hear (and, we hope, learn from) the entire Torah.
They welcome the Sabbath and celebrate Passover.