What does an asterisk mean in chemical equations?

The asterisk indicates a coordination complex, or a hydrate, in the case of water. It is a structure composed of a central compound, bonded to multiple molecules called ligands. In your example, (NH4)3PO4 is the central compound, with 12 MoO3 molecules bonded to it. You will treat the structure in its entirety as a single compound, when balancing the chemical equation.