Almost 100% of fiction out there dealing with space travel ("almost" because there are a few exceptions, mostly some sci-fi novels where the author knows better) with respect to the "magical" limit of the speed of light.
Basically, most sci-fi authors only know the "headline" version of the theory of relativity. Namely: You can't travel faster than the speed of light (in vacuum), period. (Not by any conventional means, at least.) Thus to get past this annoying limit, they invent all kinds of fictitious modes of travel, such as "hyperspace" and "warp speed" and whatnot.
They seem to think that, for example, if you wanted to travel from Earth to Alpha Centauri, it would take you at least 4.3 years to get there (using conventional means of travel), no matter what. It's (according to their limited understanding) physically impossible to get there faster. Likewise if you wanted to travel to the Andromeda galaxy, it would take at minimum 2.5 million years. In fact, the vast majority of people think like this.
It's not that simple, though, and the misunderstanding stems from not understanding the theory of relativity properly. The best example of why they don't understand it is that they have often heard of the so-called "twin paradox" but they don't understand what it means or how it works. (The "twin paradox" is the seemingly paradoxical prediction of the theory of relativity that if a person were to travel at a great speed away from Earth and then return, that person would have aged less than their twin who stayed on Earth the whole time. The seeming "paradox" comes from the question of why it's the traveling twin that ages less and not the one who stayed, even though the situation seems symmetrical from both of their perspectives. The answer lies on the changing frames of reference of the traveling twin.)
The fact is: There's no limit to how fast you can reach a distant point in space. You could travel from here to the Andromeda galaxy in one second. (This of course requires you to travel really, really close to the speed of light, but at no point would you be outrunning light.)
The vast majority of people would immediately protest to that claim, and say that it would break the prediction of the theory of relativity. This is rather ironic because relativity precisely says what I just wrote above. There's a great misunderstanding here.
The point is: Even if you are traveling from here to Andromeda in one second, you would at no point be traveling faster than light. At no point would you outrun a photon that was sent there at the same time. (In fact, if you were to measure the speed of that photon, you would measure it to be exactly c, even though you yourself are traveling at almost c, which seems really contradictory. But that's just how relativity works.) In fact, from light's own perspective it takes 0 seconds to reach Andromeda. In other words, from the light's perspective it takes no time at all to arrive there. Again, it seems unintuitive, but that's just how it is.
However, from Earth's perspective it will take you 2.5 million years to reach Andromeda. In other words, if you were travel from here to Andromeda in 1 second and then back in 1 second, you would encounter an Earth that's 5 million years older than when you left (even though you have only aged by 2 seconds.) That's how relativity works.
There is, however, a practical reason why you couldn't travel from Earth to Andromeda in 1 second: Inertia. The acceleration required to reach the necessary speed would be so immense that it would squeeze your atoms together (probably causing a thermonuclear explosion when your atoms fuse together due to the acceleration.) You (and your ship) would be completely annihilated in a fraction of a second.
To understand how big of a problem this is, assume that you were to travel just to Alpha Centauri in a spaceship that first accelerates at a comfortable rate of 9.8 m/s2 (ie. you would experience the same acceleration as on Earth) to the mid-point, and then decelerates at the same rate until it stops at Alpha Centauri. It would take you a bit over 3 years to get there like this. To get there faster you would need to accelerate more, which would become the more uncomfortable the faster you wanted to reach your destination. (The human body also probably would start showing adverse effects if exposed to unnaturally high acceleration for prolonged periods of time.)
The biggest problem reaching distant stars and galaxies is not, thus, any limit in speed (at least if you ignore that Earth will start aging much faster than you), but the limits imposed by inertia on the travelers (and the spaceship itself.) Of course there's also the question of how to produce all the energy needed to reach these speeds (which is also a rather big limiting factor), but that's another question entirely.
The only way to achieve this would be to somehow nullify inertia. As far as I know, modern physics knows of no phenomenon that could be used to achieve this. (Hypothetically you could ostensibly bend space in a manner that causes you to "fall" towards the desired direction. Thus you would be "free falling" and not accelerating, and hence inertia wouldn't be a problem. However, as far as I know, there's no known mechanism to bend space like this. And even if there were, it would probably require impossibly large quantities of energy.)