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Spherical aberration is a type of aberration (distortion) in the image of an optical instrument (such as a telescope) due to the shape of a mirror or lens. The image made by a parabolic mirror is truer than one with a spherical curvature, and the additional distortion of the latter is termed spherical aberration. Lenses of various shapes show the same issues.
A paraboloid mirror focuses light that's arriving perfectly parallel to its optical axis to a point (ignoring diffraction, i.e., the Airy disk), and has a characteristic aberration for point sources off the line of the axis. Near its vertex, the curvature of a parabola is quite close to that of a sphere, and a spherical mirror approximates what a paraboloid mirror accomplishes, but the further from the optical axis, the more the sphere-shape diverges from a paraboloid and focuses light to the point in space further from the mirror, which on the focal plane, turns a point source in the image into a finite-sized spot. This distortion is spherical aberration. The larger the percentage of a sphere that the mirror represents, the more it diverges from a paraboloid and the greater this aberration, and one way to limit it is to shape the mirror as only a small percentage of a large sphere, which is another way of saying "use a longer focal length". Spherical mirrors are easier to construct, so there is a quality trade-off regarding the resources you put into a telescope's construction. Schmidt cameras use a spherical mirror, compensating for it somewhat with a purpose-built lens (Schmidt corrector plate) but it creates its own problem: a non-flat focal "plane".