Wither means to shrivel up or shrink. If you forget to water your plants for six weeks, they'll wither — they'll dry up and you probably won't be able to bring them back to life.
Wither comes from the Middle English word wydderen, meaning "dry up, shrivel." In addition to shrinking, the verb wither can also refer to losing vitality and fading away, like people who wither as they age. They slowly lose their physical stamina and grow feeble. People also start to physically shrink at a certain age. In that way, they wither in both senses. Not only do they wither by losing their youth, they also wither by shrinking.