Eggshell and satin sit between matt and gloss, with a low-to-moderate sheen that reflects a small amount of light — this gives a slight depth to the colour without the strong reflections of gloss, and is generally more wipeable than matt.
These finishes contain enough binder relative to pigment to form a partly smooth film, so a proportion of light reflects coherently while the rest still scatters. That mixture is what produces a low sheen: enough directional reflection to give the colour some depth, not enough to create the mirror-like highlight of gloss.
Matters most on woodwork, trim and doors, where durability and cleanability are needed and the areas are small enough that sheen reads as quality rather than glare. Also matters on kitchen and bathroom walls. Matters least on ceilings, where any sheen picks out unevenness under light raking in from a window.
Using eggshell across a large wall that has been patched or skimmed unevenly. The sheen turns every filled area and roller lap into a visible mark that matt would have concealed entirely.
Practical advice
A common mid-point choice for woodwork, trim or walls in rooms that need to be cleaned regularly, such as kitchens and hallways, without going as reflective as gloss.
Always confirm with a physical sample in the actual finish before committing to a large surface — see methodology.