A Position Angle indicates a direction across the Celestial Sphere. It is analogous to compass points regarding directions on Earth (such as East-Northeast), but is for directions in the sky. The position angle of a direction at a particular point is the angle between that direction and a great circle through the point and the celestial north pole.
Such a position angle would be used to describe the direction of Proper Motion of a star.
It is also used in describing an object based upon another. For example, Guide Stars are stars whose exact position has been measured and recorded, for use in confirming which part of the celestial sphere you are looking at, such as to adjust and correct the aim of your telescope/instrument. Catalogs of guide stars such as the Guide Star Catalog, have been assembled for this exact purpose. To attempt to observe something more obscure, its position might be given in terms of a position angle from a guide star, plus an angular distance from the guide star.