Ionic compounds have high melting and boiling points because the ionic bonds that hold the compounds together are very strong and require a great deal of energy to break apart. A higher temperature indicates that more energy is being used. This extra energy is needed to break the electrostatic attraction that is present in an ionic bond.
Ionic bonds are formed when a cation and an anion come together to form a molecule. A cation is an ion with a positive charge, and an anion is an ion with a negative charge. Ions of different charges are attracted to one another. the stronger the attraction between them, the higher their melting and boiling points.
Covalent bonds are considered to be much weaker than ionic bonds due to the lack of electrostatic attraction.