In terms of the structure, simple covalent substances are made up of molecules. These molecules are bonded together by a shared pair of electrons, which forms the strong covalent bond. Between molecules, weak intermolecular forces hold the molecules in either a solid, liquid or gaseous arrangement. In order to melt/boil simple covalent substances, only the weak intermolecular forces have to be overcome, which requires little energy. As a result, simple covalent substances generally have low melting/boiling points.
Giant covalent substances, such as diamond, contain many strong covalent bonds in a 3D lattice structure. Between each carbon atom in diamond, there are 4 strong covalent bonds. In order to melt/boil diamond, a very large amount of energy is required to break these strong covalent bonds, which results in very high melting/boiling points.