Plaster of paris hardens by

 When plaster of paris is mixed with water plaster of paris takes up water of crystallization to form calcium sulphate dihydrate.

This sets to a hard mass which is monoclinic calcium sulphate dihydrate which is also called as  gypsum. Thus gypsum is the final product of setting of plaster of paris.

The reaction is as follows:

${\mathrm{CaSO}}_4·1/2{\mathrm{H}}_2\mathrm{O}+11/2{\mathrm{H}}_2\mathrm{O}\to {\mathrm{CaSO}}_4·2{\mathrm{H}}_2\mathrm{O}$

Therefore plaster of paris hardens by combining with water.