Why is magnesium oxide basic?

Magnesium oxide is a base because it can produce hydroxide ions in solution. (The definition of a base by Bronsted-Lowry is that it is a proton (that is, a hydrogen ion, because hydrogen ions have no neutron and have lost their electron, so they are just left with a proton) acceptor.

MgO+H2O ---- Mg+2OH

Therefore, it produces hydroxide ions in solution.