Shutter speed is a duration, usually written as a fraction of a second: 1/1000, 1/250, 1/30. The shutter opens, light lands on the sensor, the shutter closes. A fast shutter gives the sensor a brief glimpse; a slow one gives it a long stare.
The creative consequence is motion. At 1/1000 a sprinting dog freezes mid-stride with every hair distinct. At 1/15 the same dog smears into a streak. Neither is wrong — blur communicates speed, and freezing communicates detail. Sports and wildlife work lives at the fast end; light trails, waterfalls, and moody night scenes live at the slow end.
The practical floor is handshake. Below roughly 1/60 of a second, ordinary hand tremor starts softening the whole frame, not just the moving subject. Stabilization buys back a few stops, but the old rule of thumb still holds: keep your shutter at least as fast as one over your focal length, or brace against something solid.