Question

"carbon is tetravalent in nature".what does it mean?

Answer 1

Carbon is tetravalent in nature it means that it has the valency of 4 and thus it form 4 bonds to complete it valence shell with four electrons. 

Answer 2

Carbon is a nonmetal with electronic configuration 1s²2s²2p². It has 4 valence electrons. So the valency of carbon is 4 that is the combining  capacity of carbon is 4.
Thus it involves in covalent bonding by sharing its four electrons to form four covalent bonds . Hence carbon is tetravalent in nature.