A Stihl chainsaw uses a star-shaped sprocket to help turn the chain during operation. This drive sprocket comes under enormous stress and friction from the high speeds the chain spins at. If this sprocket won't turn inside the clutch, the chain won't spin along the bar and you can't cut.
The sprocket sits on the crankshaft underneath the clutch drum on Stihl chainsaws, which puts all the pressure from the crankshaft and chain onto the sprocket. Since the speeds of most Stihl saws reaches above 12,000 rpms, the force applied is quite significant. This force will cause the teeth on the sprocket to grind down until the chain can no longer catch. The sprocket may still spin at this point, but your chain probably won't.
Worn Needle Cage
Inside the sprocket is a bearing called the needle cage, which rides along the crankshaft stub and helps the sprocket to spin. Often these bearings will get worn out or freeze up in the cage. You can check if the bearing needs replacing by holding it up to your ear and shaking it back and forth. If you can hear the bearings rattling slightly, your needle cage is fine; if you can't hear it, you'll need to replace the needle cage.
Every time you remove any of the clutch parts, you need to lubricate the needle cage's bearing with an all-purpose engine grease. You can apply this grease with your fingers and coat the entire outer rim of the bearing. You also need to follow the lubrication schedule, which is about 20 to 30 operational hours.
Worn Clutch Assembly
The sprocket sits above the clutch assembly, which contains the clutch hub, clutch springs and clutch shoes. These parts use the centrifugal force generated from the running crankshaft to apply outward force to the sprocket. If the clutch assembly isn't spinning along the crankshaft properly, you'll lose motion on the sprocket and then your chain. You'll start to hear slight grinding or whining noises coming from the clutch area when these parts start to go.
Worn or Stuck Brake
The chain brake attaches the front safety handle to the clutch. When you activate the chain brake, a spring engages a cable, which halts the forward movement of the clutch. If your sprocket and clutch seem frozen and won't spin, you should check the function of your brake spring, the lever and arm the spring uses to pivot on and the brake cable, which connects to the clutch.
If you've removed the clutch parts and checked that the brake isn't on, and your sprocket still won't budge, try spinning the crankshaft stub. If you can't get to the stub to spin, the chainsaw likely has a seized piston that's frozen in the cylinder.