The "Crisis of the Third Century" in the Roman Empire came about for two reasons. One was an internal reason and one was an external reason.
Internally, the crisis came about because of the rise in the influence of the military in politics. This started with Septimius Severus's rule and that of the other Severan rulers. These men built up the power of the military and gave it more political clout by doing things like putting military men in high government positions. This led to a period of about 50 years in which military men, wanting to be emperor, caused chaos as they fought one another. There were 22 emperors in those 50 years and 20 of them died violently.
Externally, the crisis came about because of barbarian invasions. These invasions probably came about at least in part because of the weakness brought on by the internal strife. The Sassanid Persians invaded as did the Germanic tribes. This added to the chaos of this century.