To stiffen is to become stiff or unbending. If your legs stiffen during a long plane flight, you'll want to stretch them out once you land.
You can stiffen something deliberately, like when you stiffen a package with cardboard to protect it in the mail. You can also stiffen in reaction to something: "The spooky creaking sounds upstairs made us stiffen in terror." The earliest sense of this verb was "make steadfast," from a now-obsolete meaning of stiff, "gain strength."