The actual science behind the idea of time travel is incredibly difficult for me to wrap my mind around. It seems to be the case that both time and space are relative and related. As a result, time does not pass in a uniform manner and instead is relative to one's speed with respect to light (or indeed gravity, which affects space). Differences in gravity and speed have been shown to result in differences in the passing of time, such that a very accurate clock on the top of a tall building registers time's passage more slowly than another very accruate clock at ground level (though it is an astonishingly small difference).
If time is a function of space, then it would stand to reason that time is directly related to speed. Since the fastest known thing in the universe is light (which provides the only known physical speed limit), the common assumption is the best one can do is slow the passage of time as one cannot actually exceed the speed of light. Everyone technically travels "through time" it's simply done in the same direction and therefore not terribly intresting. Were one able to do so, the concept of time itself no longer has a meaning as it is no longer related to anything in particular, which may indeed mean one can travel about in an arbitrary direction in time.
The trouble is, the amount of energy required to accellerate any object with mass to the speed of light is actually more than the sum total energy in the universe (which itself strikes me as strange, but I digress). However, since speed is a function of space and time, it stands to reason that if one can manipulate space, they could also manipulate time itself. This point is given some degree of crediblity since gravity has been proven to affect both light (the experiment that first corborated Einstein's theory) and time (in a series of famous experiments wherein fantastiaclly accurate clocks were placed at different distances from the center of the earth). The idea of manipulating space itself is at the core of most science fiction faster than light travel, from the idea of "wormhole" travel to star trek's "warp travel". Mass effect is notably different in that they discovered an element who's mass is arbitrary. Since this material has no fixed mass, a lot of the usual physical conventions get thrown out the window.
As an aside, there are things that travel faster than the speed of light...sort of. Sound, itself nothing more than a wave carried through some medium or another, could concievably (and in a recent experiment my indeed) travel faster than light. The catch is, though a sound wave requires motion of a medium, the medium itself doesn't not actually travel - only the energy of the wave does.
But, like I said, the physics explanation of the concepts are incredibly difficult for me to wrap my mind around as it requires thinking in four dimensions if nothing else. Stephen Hawking's "A Brief History of Time" actually covers the topic at length, and even in a book written for the masses it's difficult. When the concept comes up as a point of discussion in my various math/physics classes and we start delving into the mathematics of it all it seems like a simpler concept in general (if only because I understand the rules of math whereas I cannot think in four dimensions).