Why furniture leaves dents
A heavy piece of furniture standing in one spot presses the carpet pile down for so long that the fibres stay crushed when you move it. The carpet is not worn or damaged — the tufts are simply compressed and matted flat — which is why the fix is to relax and lift them, not to clean anything.
The ice-cube method, safest for any carpet
The simplest fix is an ice cube — one, or a few for a big dent. Set it in the crushed area and let it melt completely, an hour or two, so the carpet slowly absorbs the cold water and the compressed fibres swell and stand back up. Blot up any excess with a towel, then work the pile up with your fingers, a spoon or the edge of a coin. Because there is no heat, this is safe on almost any carpet.
The steam method, faster but with care
For a quicker lift, steam relaxes the fibres. Lay a damp towel over the dent and hold a steam iron just above it — not touching — or use a garment steamer, letting the warmth soak in for a few seconds, then fluff the pile up while it is warm. Keep the heat moving and never press the iron onto the carpet: direct heat can melt or glaze a synthetic pile. If you are not sure what the carpet is made of, use the ice method instead.
Fluff and finish
However you relax the fibres, finish by lifting them. Rub the pile back up with your fingers, a stiff brush, the edge of a coin or the tines of a fork, working in different directions until the tuft stands level with the carpet around it. A vacuum pass afterwards helps set the pile upright, and a deep, old dent may take a second round.
Stopping dents before they start
Dents are easier to prevent than to fix. Shift heavy furniture a little every so often so its weight does not sit on the same tufts for months, put furniture coasters or cups under the legs to spread the load, and rotate furniture and rugs when you clean. The same crushed-pile trick works on a rug — a little moisture and a fluff bring it back.