The symbol Xi where X is an extensive property of a homogeneous mixture and the subscript i identifies a constituent species of the mixture, denotes the partial molar quantity of species i defined by
X can be: Volume, mass, entalphy, entrophy...
A partial property is the contribution of that property that a substance make when is part of the mixture.
e.g. The partial molar volume is the contribution to the volume of the mixture that a subtance makes when it is part of the mixture.