Carbon is a key component of all known life on Earth. Complex molecules are made up of carbon bonded with other elements, especially oxygen, hydrogen and nitrogen, and carbon can bond with all of these because of its four valence electrons. Carbon is abundant on Earth. It is also lightweight and relatively small in size, making it easier for enzymes to manipulate carbon molecules. It is often assumed in astrobiology that if life exists somewhere else in the universe, it will also be carbon-based. Critics refer to this assumption as carbon chauvinism.
"What we normally think of as 'life' is based on chains of carbon atoms, with a few other atoms, such as nitrogen or phosphorus", per Stephen Hawking in a 2008 lecture, "carbon [...] has the richest chemistry." The most important characteristics of carbon as a basis for the chemistry of life are, that it has four valence bonds, and that the energy required to make or break a bond is at an appropriate level for building molecules, which are stable and reactive. Carbon atoms bond readily to other carbon atoms; this allows the building of arbitrarily long complex molecules and polymers.
There are not many other elements which even appear to be promising candidates for supporting life, for example, processes such as metabolism. The most frequently suggested alternative is silicon. Silicon is in the same group in the Periodic Table of elements, and has four valence bonds, and bonds to itself, generally in the form of crystal lattices rather than long chains. It is considerably more electropositive than carbon. Silicon compounds do not readily recombine into different permutations in a manner that would plausibly support lifelike processes.