The two characteristics of carbon that enable it to form a large number of compounds are:
Catenation: It is the property of carbon atoms to form covalent bonds with other carbon atoms and form long chains. These chains may be straight, branched, or may even result in the formation of rings. Carbon atoms may be linked to each other by single, double, or triple covalent bonds.
Tetravalency: Valency of carbon atom is four. This enables the carbon atom to form bonds with other atoms such as oxygen, sulphur, and hydrogen. These bonds formed by carbon are very strong. This can be attributed to the small size of the carbon atom.