In the story of the three little pigs, only the house made of brick was able to withstand the huffing and puffing of the Big Bad Wolf. To withstand is to hold up against something strong.
Withstand means to stand your ground against a powerful and negative force. A lot of toys can withstand rough treatment, but CDs definitely can't. And hopefully, you can withstand the pressures of school and work! If you can withstand a lot of criticism, it means you can take it without giving up.