Carbon forms a large number of compounds due to:
Property of catenation
Carbon has a strong tendency to form pπ−pπ multiple bonds either with itself (C=C)or(C≡C) or with other elements of similar size (C=O,C=N,C≡N). This is due to small size and high electronegativity of carbon. The extent of overlap which can result in multiple bond formation is maximum in case of C, i.e. in C = C, it is 2P orbital of C overlapping sideways with 2p orbital of C.
Down the group (↓), the tendency to form pπ - pπ bond decreases drastically due to increase in size and decrease in electronegativity of the atom. The interaction of 3p orbital of silicon and 2p orbital of atom of the second row element (carbon, nitrogen, oxygen) will result in much poor overlap and hence a weaker bond.
The ability of forming bond with itself is known as catenation.
This is the property because of which carbon can form many compounds.