Sheen is the amount of light a dried paint film reflects. Flat hides wall imperfections and looks soft, but it scuffs easily and is hard to wipe clean. At the other end, semi-gloss reflects a lot of light, shrugs off scrubbing, and shows every bump in the drywall underneath.
For most living rooms and bedrooms, eggshell is the safe middle: a slight glow, easy to touch up, and tough enough for normal life. Ceilings almost always get flat, because a ceiling with sheen shows roller marks and every seam in the drywall.
Kitchens, bathrooms, laundry rooms, and kids' rooms earn satin. It handles moisture and wiping better than eggshell without looking shiny. Trim, doors, and cabinets get semi-gloss, which gives them crisp definition against the walls and stands up to hands and vacuums.
One more thing: the same color looks darker and richer in a higher sheen. If you fell in love with a swatch, ask for a sample in the sheen you're actually going to use, and look at it in the room, in the afternoon, before committing.