The verb suffer means to feel pain or something equally unpleasant. You'd probably do anything you could to be sure your beloved cat didn't suffer when she got old and sick.
You can suffer from the pain of a broken leg, but you can also suffer from shyness, regret, poverty, or any number of unpleasant things. You can even describe something that becomes worse using the word suffer, like when someone's grades suffer during soccer season. The root of suffer is the Latin word sufferre, to bear, undergo, or endure. That's why someone who doesn't suffer fools gladly won't put up with nonsense.