Why ionic compounds have high melting points?

Think table salt, NaCl

The Na has given up an electron to the Cl so the Na end of the molecule is charged + while the Cl end of the molecule is charged -. The molecule is "polar".
That gives a good grip to the next molecule whose - side sidles up to our + side and grabs hard.
Therefore every molecule has a good grip on the next one and it is hard to make it flow like water without losing that grip by pumping a lot of heat energy in.