To whimper is to make a low, pitiful whining sound. If you've ever heard a sick puppy cry, you know what it means to whimper.
Use the verb whimper to describe the crying you do when you're frightened or in pain. A child with a fever might whimper, or a woman with a terrible migraine headache. It can also be a noun, although in that case the word takes on a bit of a whiny meaning: "The boy gave a whimper when he realized he was only getting one cookie." Whimper is onomatopoeic, or a word that sounds just like what it means.