Silicon is the element in the periodic table that has the symbol Si and atomic number 14. It is the second most abundant element in the Earth's crust, making up 25.7% of it by mass. Silicon is the principal component of most semiconductor devices and, in the form of silica and silicates, in glass, cement, and ceramics. This abundance it part of the reason why the Urbankans came to Earth. (DW: Four to Doomsday)
Though not as common as carbon-based life, there are some silicon-based species in the Universe. Silicon-based life generally looks like rock, is very tough and breaks down into sand when it dies. According to Article 7954 of the Galactic Charter, Silicon-based life-forms must not be moved from their planet. (DW: The Stones of Blood)
Silicon-based life is found in other science fiction, owing to the fact that carbon and silicon form the same number of molecular bonds with other elements. Silicon-based life is scientifically possible, but no real-world examples have been found.
Silicon-based lifeforms were considered a fantasy by the Federation until first contact with the silicon-based Horta of Janus VI in 2267 (TOS episode: The Devil in the Dark). In 2370, when Julian Bashir was attempting to locate a Horta in the mines of Davonia his tricorder had trouble singling it out as the mines had been drilled with high-powered phasers causing the walls to turn into glass, making the silicon lifeform difficult to detect amongst all the other silicon in the area. (DS9 novel: Devil in the Sky)
In real-life, Silicon presents similar chemical properties to Carbon and the possibility of existing (extraterrestrial or not) life-forms has been ventured both in theory and science fiction.