Carbon-based life
Carbon forms the key component for all known life on Earth. Complex molecules are made up of carbon bonded with other elements, especially oxygen, hydrogen and nitrogen, and carbon is able to 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.
Characteristics
"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, that the energy required to make or break a bond is at an appropriate level for building molecules, which are stable and reactive. Because carbon atoms bond readily to other carbon atoms allows for the building of arbitrarily long complex molecules and polymers.