Aberrations are defects in images produced by a telescope (or optical system). They are caused by limitations in the design and manufacture of the optics. Designers and optical factories strive to produce affordable telescopes that have as few aberrations as possible.
Two major aberrations seen in telescopes are spherical aberration and coma.
Spherical aberration is caused by rays of light passing at different distances from the center of a lens or mirror not coming to the same focus. Edge rays will typically come to a focus closer to the lens or mirror than central rays. Corrector plates in Schmidt-Cassegrain telescopes are designed to fix this aberration. Coma is a related effect: it is spherical aberration from rays that come in off-axis. It shows up as little off-axis comet-shaped blobs that point inwards towards the center of the field and that get bigger as you look towards the edge of the field of view.
Aplanatic optics are designed to eliminate both spherical aberration and coma. They are superior to SCT optics that rely only on the corrector plate, since the corrector only gets rid of the aberrations in a small area around the center of the field of view. This is especially important for astrophotography, where coma towards the edges of an image can be very noticeable.
The end result is sharper images across a much wider field of view than in other designs. EdgeHD aplanatic optics maintain diffraction-limited images across the entire field of view of many of the most popular astrophotography cameras.