Something that's inescapable is impossible to get away from. A reluctant swimmer may stop trying to talk his mom out of making him go to swimming lessons once he realizes that learning to swim is inescapable.
Any force or occurrence or duty that you just can't avoid is inescapable. Feeling angry at people you love sometimes is inescapable, and children growing older is also inescapable. The adjective combines the prefix in, or "not, the opposite of," with escapable, which comes from the Vulgar Latin word excappare, literally "get out of one's cape," or "leave a pursuer holding just one's cape."