Containment is a way to keep something bad from spreading. If you get chicken pox, you won't be allowed back in school until you're not contagious anymore. Your school's aiming for containment of the disease by keeping you away from everyone else.
Containment is also a foreign policy strategy. If one country is stirring up trouble by sending weapons and fighters into neighboring countries, other countries can join together and enact a policy of containment, to isolate the rogue country and keep it from causing chaos outside its borders. In a nuclear reactor, the containment system is the back-up system that's supposed to keep dangerous radiation from leaking out into the atmosphere or water when there's an accident.