There are several, but one of the more important ones is that it's not terribly energetically unfavorable for a carbon atom to form single bonds with other carbon atoms as opposed to forming bonds with oxygen or hydrogen (the most abundant elements in the Earth's crust and in the universe as a whole respectively). For why this is important, read the essay The One and Only by Isaac Asimov; it's in his non-fiction book The Tragedy of the Moon.
Carbon can form an infinite number of combinations and is the base of life.
Proteins
diamonds and graphite are the same as they are made of the same element: carbon. what makes them so different in apperance is the different way the carbon atoms are bonded.
Coal is an organic sedimentary rock. It has conchoidal fracture. The composition is so different because coal, depending on age, contains mostly carbon as it is formed from plant cellulose. It is different because it is carbon, as opposed to a common mineral like other sedimentary rocks.
High carbon steel is a metal.The addition of carbon makes the steel harder after heat treatment.
it makes it hot
thermal and electrical conductivity
Proteins
Well, nonmetals are opaque and brittle. They are also bad conductors of heat and electricity.
metals nonmetals
this makes ionic bonding.
Tetravalence, Carbons ability to form four bonds with other atoms
Higher frequency, higher pitch.
The ability of each carbon atom to form covalent bonds, including bonds to other carbon atoms. This makes possible chain hydrocarbons of any length.
Carbon has 4 valence electrons, so it has lot of bonding options. This makes possible the huge diversity of compounds that involve the element carbon, which in turn, makes possible the organic compounds that make life possible.
diamonds and graphite are the same as they are made of the same element: carbon. what makes them so different in apperance is the different way the carbon atoms are bonded.
Oxygen and carbon are both nonmetals that have a strong preference for creating covalent bonds (bonds where electrons are shared between the atoms). They are also both relatively abundant, so they tend to be present with each other and bond through covalent bonds.
Each of two or more different physical forms in which an element can exist.