The virial equation provides both a general form for an equation of state for gases or liquids, as well as a connection (through its coefficients) to the microscopic level intermolecular forces experienced by the atoms and molecules. The equation of state can be used (along with other information) to arrive at a phase diagram. The Latin root of the word is vir which is a plural form of vis or force.
Physical chemists are quite fond of the virial expansion, as this quote might suggest:
"The virial expansion is one of the cleanest-cut developments in the subject of statistical mechnics." Condon and Odishaw in the Handbook of Physics, 1967.