When something skyrockets, it shoots up. Immediately after the Winter Olympics, interest in ice skating, bobsledding, and curling tends to skyrocket, or increase suddenly and dramatically.
The verb skyrocket is good to use when something grows or shoots up as abruptly as a firework. Gas prices, food prices, debt, and winter cases of the flu are all said, from time to time, to skyrocket. A more literal meaning of skyrocket is the actual rocket that's designed to send a flare or firework high into the sky. A bottle rocket — a firework that is placed in an empty bottle before being lit and shooting into the air — is one example of a small skyrocket.