We are commanded to remember Shabbos, but that doesn’t mean rolling over in bed and thinking, “Oh, yeah… it’s Saturday.” Rather, we are commanded to praise the day out loud, over a cup of wine. We call this “Kiddush,” meaning “to sanctify,” since that’s what we were commanded to do. Likewise, we escort Shabbos out through the analogous blessing of Havdalah, which marks the separation between “holy” time and “secular” time.
We actually say two Kiddushes on Friday night and two Havdalahs on Saturday night, as the Amidah prayer for those days includes a form of Kiddush or Havdalah as appropriate. One may not eat, however, until one has recited (or heard) the Kiddush or Havdalah over wine. (If you ever wondered how one can light the candle to make Havdalah without already having said Havdalah, that’s how: Havdalah in davening enables one to do so.)
We also have the practice to say a form of Kiddush on Shabbos day, but that is a rabbinic enactment euphemistically referred to as Kiddusha Rabbah – “The Great Kiddush.” (The only obligatory part of the daytime Kiddush is the bracha “borei pri hagafen” over the wine; all the rest is custom.)
The reason for this mitzvah is to encourage a love for and an appreciation of Shabbos. This is why it is said over wine, which is a significant beverage (as opposed to, say, soda or tea) that brings joy to the heart. (Grape juice is an acceptable non-alcoholic substitute.) In a pinch, one might be able to use bread for Kiddush or orange juice for Havdalah, but wine or grape juice is by far the preferred medium.
This mitzvah applies to both men and women, in all times and places. It is discussed in the Talmud in the tenth chapter of Pesachim. In the Shulchan Aruch, it can be found in Orach Chaim 271. It is #155 of the 248 positive mitzvos in the Rambam’s Sefer HaMitzvos and #19 of the 77 positive mitzvos that can be fulfilled today as listed in the Chofetz Chaim’s Sefer HaMitzvos HaKatzar.