A two-stroke engine completes four functions (intake, compression, power, and exhaust) in two strokes. Therefore each stroke comprises of two functions.
The cycle begins with intake of fuel into the crankcase. The opposite side of the piston compresses the fuel (of the previous cycle) until it is near the dead-centre when a spark ignites the compressed fuel. This stroke is the intake/compression stroke.
As the fuel burns, it begins its power stroke and pushes the piston in the opposite direct while delivering work. At the end of the stroke, partially compressed fuel goes to the ignition chamber (cylinder), where the exhaust port is exposed. The highly compressed exhaust rushes out the port and exhaust is completed by fresh fuel that ejects the remaining exhaust before the cycle begins again. This completes the power/exhaust stroke.
The two stroke engine is compact and powerful. However it is relatively inefficient (thermodynamically) and polluting (some of the unburnt fuel escapes with the exhaust).
