Why are ceramics strong?

Ceramics are strong but only in some ways. They are:

They resist to high temperatures, they don't conduct electricity and they have a high Young/elasticity module - that is, the deform very little while resisting to high tensions.

Atoms in ceramics are either linked by covalent or ionic bounds, which are the strongest bounds at the atomic level. Therefore they tend to have high thermal resistance since its very hard for those bounds to be broken, and so it's very hard for a ceramic to melt. That's why they're used in space shuttle.

They don't conduct electricity because there aren't free electrons or free ions capable of transmitting an electric current.