Wormholes are a slightly more credible way to evade Einstein's speed limit than a "warp drive" or "hyperspace." Imagine that you had to drive from Los Angeles to New York, a distance of 2800 miles on a map. Obeying a 70 mph speed limit, you would need at least 40 hours for the trip. But suppose you could fold the map so that New York lay directly on top of Los Angeles. Now you could drive from Los Angeles to New York in a matter of minutes, even if you were forced to obey the speed limit. This isn’t a perfect analogy, since the map is two-dimensional, and a wormhole is a shortcut in three-dimensional space. But a galactic explorer could enter one end of a wormhole and pop out at a completely different part of the universe, without ever exceeding the speed of light.
Wormholes have been featured in numerous works of science fiction, including the recent film Interstellar. The Caltech physicist Kip Thorne, who was a creative force behind Interstellar, did much of the scientific work on wormholes, and his book, Black Holes and Time Warps, gives an excellent explanation of how they work. But wormholes, like the Alcubierre warp drive that I discussed earlier, occupy a scientific twilight zone (no, not that Twilight Zone). Einstein's theory of relativity doesn't rule out wormholes, but Thorne showed that if you want to travel through a wormhole, you have to hold your wormhole open using exotic matter with negative energy density. We've never seen that kind of exotic matter, and we've never observed any wormholes themselves. So the jury is still out on the possible existence of wormholes.
In addition to providing an end-run around the cosmic speed limit, wormholes open up interesting plot possibilities. Our intrepid space explorers can no longer simply zoom anywhere they like, but have to travel along a fixed network, not unlike a city subway system. It might be easy to travel halfway across the galaxy, but impossible to visit the nearest star. A galaxy riddled with wormholes would resemble late 19th-century America, where it was relatively easy to zip from one city to another by train, but travelling outside of cities was slow, laborious, and sometimes dangerous. Planetary systems far from a wormhole would likely suffer the same dire fate as cities bypassed by the railroads or, much later, hotels and restaurants bypassed by the U.S. Interstate Highway System. (The entire KFC restaurant empire owes its existence to the fact that the Colonel Sanders's first restaurant was bypassed by the interstate. I won't comment on whether that's good or bad).
While many authors have employed wormholes as just another way to evade Einstein, others have exploited their peculiarities. Ian M. Banks’s novel, The Algebraist, opens with the protagonist’s planet cut off from the rest of civilization due to the destruction of its wormhole connection, and much of the plot is driven by a quest to uncover a secret list of wormhole coordinates concealed by a race of gas-giant dwellers. Lois McMaster Bujold explores some the cultural consequences of a wormhole universe in her Vorkosigan Saga of novels and short stories. Much of the action centers around the planet of Barrayar, which was cut off from the rest of the galaxy by the loss of its wormhole and subsequently regressed to a feudal state. So wormholes don't just let you build a galactic empire -- they funnel that empire in very specific and interesting directions.