Celestial Sphere
The celestial sphere is an imaginary sphere surrounding Earth on which stars appear to sit, used to describe positions and the daily motion of the sky.
Definition
The celestial sphere is an imaginary giant ball around Earth with all the stars painted on the inside, used to describe where things are in the sky; as Earth spins, the whole sphere seems to turn around us. Its north and south celestial poles lie directly above Earth's poles, the celestial equator is the projection of Earth's equator, and stars appear to circle the poles once a day because Earth rotates once a day. It is the reference frame for equatorial coordinates: declination, in degrees north or south of the celestial equator, and right ascension, measured eastward from the vernal equinox in hours ($24^\text{h} = 360^\circ$). The ecliptic, the Sun's apparent yearly path, is tilted $23.5^\circ$ to the celestial equator, and precession moves the equinox westward about $50$ arcseconds per year, so coordinates are quoted for a standard epoch such as J2000.0.
Example
Polaris sits almost exactly on the sphere's north pole, so it barely moves all night while other stars wheel around it. From Charlotte at latitude $35^\circ$ N, Polaris stands about $35^\circ$ above the northern horizon, stars within $35^\circ$ of the pole never set, and stars within $35^\circ$ of the south celestial pole never rise. Sirius has right ascension about $6^\text{h}\,45^\text{m}$ and declination about $-16.7^\circ$, so from Charlotte its maximum altitude is $90^\circ - 35^\circ - 16.7^\circ \approx 38^\circ$ above the southern horizon.
Key Insight
The stars are not really all the same distance away; the celestial sphere is a convenient picture, like a planetarium dome. The altitude of the celestial pole above your horizon equals your latitude, a fact sailors used to navigate for centuries before GPS. The sphere is geocentric only as a coordinate convention, the same way latitude and longitude are Earth-centered, because directions on the sky, not distances, are what a telescope must point at.