Sheen is how much light a paint film reflects, and it drives two things people care about long after the color has stopped being exciting: how much the wall shows its own imperfections, and how well it takes cleaning.
Flat and matte hide the most. On an older ceiling or a wall with a hundred years of patches under it, flat is genuinely the right answer, because a higher sheen will rake light across every ripple and make the repair work obvious. The trade-off is that flat marks easily and rarely cleans without leaving a burnished spot.
Eggshell and satin are the practical middle, and they're where most walls should land. There's enough sheen to wipe a scuff off a hallway and enough tooth to stay quiet on a wall that's not perfectly flat. In kitchens, baths, and children's rooms, satin earns its place.
Semi-gloss and gloss belong on trim, doors, and cabinetry: surfaces that get touched, need scrubbing, and benefit from a crisp line against the wall. The higher the sheen, though, the more it magnifies what is underneath, which is exactly why trim has to be filled and sanded properly before it's painted rather than after somebody notices.
One more thing worth knowing: sheen names aren't standardized between brands. One company's eggshell reflects more light than another company's satin. If sheen matters to you, look at a real sample board in the actual room, in the light that room gets, before committing a whole house to it.