A backfire ignites the fuel, or something else flammable, outside of the cylinder where it should be ignited. As gas runs into the cylinder, the coil sends up a spark to ignite the gas. When your Stihl 250 trimmer starts backfiring, this spark is either getting lost early, not reaching it at all or causing something else in the engine to ignite.
Check the Muffler
The muffler vents noxious carbon exhaust from the engine. Over time, this carbon will gradually deposit onto the walls of the muffler, the spark arrester screen and the exhaust port. If you haven't kept these parts cleaned---usually about every 90 operation hours---you may have developed build-up in the exhaust system which is igniting because of the burning fuel in the cylinder. You'll need to clean the muffler, screen and exhaust port with a brush, rag and a mild detergent. If the sludge is too thick, replace the components.
Check the Ignition Module
When the ignition coil sends the spark, it needs to travel to the plug through a circuit of wires. If these wires are loose or corroded, the spark may be jumping prematurely. Disassemble the starter, flywheel and ignition system and check all of the wires, especially the ground and short circuit wires, at the ignition module. Replace any corroded or loose wires and always make sure they are properly connected to the module, the spark plug and the ignition switch. If you suspect the ignition system and the wires haven't solved your problem, you will need to replace the entire module.
Check the Flywheel and Key
The flywheel needs to spin fast enough to build up enough magnetic energy to trip the coil to fire the spark. The flywheel spins via the crankshaft and is mated to the crankshaft through a metal key. This key can get bent slightly, causing the flywheel to spin erratically, which can prematurely fire the spark. The flywheel can also crack around the fins, which will also cause it to spin poorly and fire the spark improperly.
Check the Intake Valve
If the engine is misfiring or backfiring through the air filter or carburettor system, fuel may be leaking from the carburettor into the cylinder. This means that fuel is getting ignited before the cylinder. This can occur due to a faulty intake valve or intake manifold that's causing extra air to leak into the system. The gaskets can also dry out and crack, causing the fuel or air leak. Remove, disassemble and check the carburettor and gaskets for leaks. You'll also need to inspect the intake valve and replace if necessary.