Representing directions rather than distances
Objects at different distances can be projected along their sightlines onto one imagined sphere. Angular positions provide a convenient language for maps, direction comparisons and telescope pointing.
Projection retains direction without depth. Objects close on a sky chart can be far apart in space; distances and motions are needed to assess a physical association.
References: [1]
Poles, equator and local directions
In the common geocentric model, Earth’s axis supplies the celestial poles and its equatorial plane supplies the celestial equator. Right ascension and declination organize directions using these references.
The zenith is directly overhead and the nadir opposite it. The local meridian passes through the celestial poles and zenith. A site’s zenith is not the north celestial pole shared by the coordinate construction.
References: [1]
The model and daily sky motion
Earth’s rotation produces daily motion relative to a local horizon. A celestial coordinate description can be transformed into azimuth and elevation for a chosen site and time.
Precise pointing also needs the frame, coordinate epoch and relevant corrections. The spherical model provides a representation, rather than removing precession, source motion or changes in observer position.