Mundane science fiction, the preferred genre on this site, builds stories upon the solid rock of known science rather than on made-up science. Consequently MSF features almost exclusively stories set in our own Solar System, since with the current state of science interstellar travel will take centuries if not longer, because faster-than-light (FTL) travel is almost impossible under accepted theory of physics.
In “regular” science fiction authors have invented a whole range of methods to circumvent Einstein’s speed limit. Generally SF authors just use pseudo-scientific language to justify FTL travel in their stories, and most of these proposals can be dismissed out-hand by writers of mundane science fiction. There are only a very few methods of FTL which might be of interest for authors in this genre.
Of all proposed methods for FTL travel, wormholes are by far the most interesting candidate for MSF. Unlike its competitors wormholes are not prohibited by general relativity and hence wormholes are the most credible method for achieving FTL travel.
How do wormholes work? According to modern physics one cannot travel faster than light locally, i.e. on my way from A to B I cannot break the universal speed limit c at any intermediate point. In fact a wormhole is nothing more than a shortcut, it provides a shorter pathway than the apparent distance between A and B. While you travel through a wormhole you will never break the speed of light, though for outside observers it would appear you moved faster than c.
The general motivation for wormholes is that the ordinary space we live in, is somehow folded and hence there should be shorter paths if we could traverse through higher dimensions.
Nevertheless wormholes have several disadvantages for writers of mundane science fiction. Though wormholes are allowed under current physical insights, no one has ever proved they actually exists. Further physicists believe that in order to use wormholes exotic matter or negative energy is required to open wormholes. And till now, no one has achieved to produce these substances nor has anyone proposed a practical method to create these.
However, if wormholes would be proven to be practical, they are interesting for several reasons beyond interstellar travel. First wormholes could be used within our own Solar System to reduce travel time. Even if this would not result in FTL travel, shorter distances are desirable.
Also wormhole would give an opportunity to “hide” in space. Since wormholes are outside the observable universe, outsiders cannot see what is inside. At best they can see that something suddenly disappears and unless they are aware of the endpoint of the wormhole they cannot know where the object is going to. This might an advantage in military operations, but also allows space pirates to conduct surprise attacks.
My advice to writers of mundane science fiction who have a slight interest in FTL travel, is to stick with wormholes. They are our best chance at FTL given our current understanding of physics.