Step 1: Picture the structure of an ionic solid.
An ionic compound is not made of loose molecules, it is a giant three dimensional lattice where positive and negative ions are packed together in a fixed repeating pattern.
Step 2: Think about what holds that lattice together.
Every positive ion is surrounded by negative neighbours and every negative ion by positive neighbours, and these opposite charges pull on each other by strong electrostatic attraction, following Coulomb's law: \[ F = k\frac{q_1 q_2}{r^2} \] This pull acts throughout the entire crystal, not just between one pair of ions.
Step 3: Connect this to melting.
To melt a solid, you must free the particles from their fixed positions so they can move past each other. Since the electrostatic pull holding the lattice together is so strong and spread across the whole structure, a large amount of heat energy is needed to break enough of these bonds for the solid to melt.
Step 4: Conclude.
This is exactly why ionic compounds have high melting points, the strong electrostatic forces between ions demand a lot of energy to overcome. \[ \boxed{\text{Strong electrostatic attraction between ions needs high energy to break}} \]