If something endures, it lasts: Beethoven's fame has endured for more than 200 years. But if you endure something, you suffer through it: We endured our teacher's slide shows of her vacation photographs.
Notice above that something that endures can be good or bad. Something you endure is always bad. And people are forever talking about what they can't or won't endure, as in "I refuse to endure any more abuse from my neighbors." Endure derives from the Latin indūrāre "to make hard," formed from the prefix in- "against, into" plus dūrus "hard."