Why do ionic compounds have high melting and boiling points?

Ionic compounds are formed by strong electrostatic forces of attraction between oppositely charged ions. These forces are very strong and extend throughout the entire crystal lattice. 

A significant amount of energy is required to overcome these strong inter-ionic forces and break down the crystal structure, allowing the ions to move freely (melt) or separate completely (boil). 

Therefore, ionic compounds typically have high melting and boiling points.