Something that's been cut or pierced with something sharp is punctured. A punctured tire will quickly go flat and need to be repaired or replaced before you can drive your car again.
A bad accident can cause a punctured lung, a serious injury that may require surgery, since the lung actually has a hole in it. A punctured balloon is much less serious, but can cause plenty of tears on the part of the child who was holding it. And more figuratively, a dancer's punctured (or collapsed) hopes and dreams might result from a ballet teacher's negative comments. The Latin root is punctus, "pricked or pierced."