The celestial sphere is an imaginary sphere of gigantic radius, centered on the Earth. All objects which can be seen in the sky can be thought of as lying on the surface of this sphere.
Of course, we know that the objects in the sky are not on the surface of a sphere centered on the Earth, so why bother with such a construct? Everything we see in the sky is so very far away, that their distances are impossible to gauge just by looking at them. Since their distances are indeterminate, you only need to know the direction toward the object to locate it in the sky. In this sense, the celestial sphere model is a very practical model for mapping the sky.
The directions toward various objects in the sky can be quantified by constructing a Celestial Coordinate System.