HaShem commanded the Jewish people to make the seventh day of the week holy. This is Shabbat. The other six days of the week are for work, and Shabbat is for rest. Just as, after creating the world in six days, HaShem rested on the seventh day, so do we stop our creative work on Shabbat.
Shabbat is honored with prayer, Torah learning, conversation, and spending time with family. We make kiddush over wine or grape juice, we eat fresh, delicious challah, and we enjoy extra-special foods. During the week, we think about Shabbat and prepare for it by buying food and wine, cleaning our houses, and making sure that our best clothes are clean and ready.
Even the Hebrew names for the days of the week show that we're thinking about Shabbat all week long. Instead of saying "Sunday, Monday, Tuesday..." we say "Yom Rishon (the first day), Yom Sheini (the second day), Yom Shlishi (the third day)..." In this way, we count the days until we reach the high point of the week: Shabbat!
A story is told about the great Sage by the name of Shammai. When he would see a particularly appetizing piece of meat at the butcher shop during the week, he'd buy it in honor of Shabbat. Every day he would find a piece of meat that was even more tender and tasty-looking than the meat he had bought the day before. Each day, he would ask his wife to cook the meat from the day before, so it wouldn't go to waste. That's why it was said about Shammai, that every day he ate in honor of Shabbat!