Carbon makes four bonds, and it makes them readily to itself. Chains, branches, rings and sheets of carbon atoms are all stable at the temperatures at which liquid water exists, and each carbon left over can carry hydrogen, oxygen, nitrogen, sulfur or phosphorus. No other element combines that versatility with that stability. Silicon, directly below it and often proposed as an alternative basis for life, forms weaker bonds to itself, and its dioxide is a solid rather than a gas, which blocks anything resembling a respiratory cycle before it starts.
The consequence is that the chemistry of carbon compounds is a subject in its own right, larger by number of known substances than all the rest of chemistry together. Proteins, sugars, fats and nucleic acids are all carbon frameworks. The distinction between organic and inorganic chemistry was originally a claim that the first required a vital force; Friedrich Wohler's synthesis of urea from ammonium cyanate in 1828 removed the claim and left the name behind.
Carbon is only about 0.02 per cent of the Earth's crust, far less abundant than oxygen, silicon, aluminium or iron. Living things concentrate it enormously. The carbon cycle moves it between atmosphere, ocean, rock and biology on timescales running from days to hundreds of millions of years, and the current alteration of that cycle by burning fossil carbon is the central environmental fact of the present.
Carbon-14, made continuously in the upper atmosphere by cosmic rays and taken up by everything alive, decays with a half-life of about 5,730 years. Willard Libby's radiocarbon dating, developed from 1946, made it possible to put absolute dates on organic remains for the first time, and reordered a great deal of archaeology in the process.