Aluminum Sulfate is ionic. It's made up of the aluminum ion, `Al^3^+` , and the polyatomic ion sulfate, `SO_4^2^-` . Rather than existing as discrete molecules it exists as a crystal lattice of aluminum and sulfate ions in the ratio 2:3, held together by electrostatic charges between positive and negative ions. The ratio is due to the two different charges. The simplest formula of an ionic compound has a net charge of zero; in this case 2(+3) and 3(-2) add up to zero. The size of the ions and their charges help determine the type of crystal structure that will form.
Molecular compounds, on the other hand, are composed of molecules in which the atoms of each molecule are held together by strong covalent bonds but the molecules usually aren't significantly attracted to each other due to lack of charges. They tend to be gases or have low melting and boilling points. One exception to this is covalent network bonding, such as what occurs in diamond and silicon dioxide (quartz). In this case the covalent bonds occur between atoms in multiple directions, creating a crystal lattice. These substances have high melting points and aren't considered molecular.