The phrase "suspension of disbelief" was first used by Samuel Taylor Coleridge back in 1817. The basic idea is simple - fiction relies on the observer willingly accepting something false. It's a pretty rare work of fiction that expects people to believe that it's actually true. For the vast majority of fiction, the consumer knows going in that they're seeing something unreal.
|Samuel Taylor Coleridge|
I find that I rarely have trouble with the sheer amount of things that a work of fiction expects me to accept. Magic, aliens, super-spies, warp speed, etc, etc...it's all good. Suspending my disbelief rarely runs into a volume limit. Give me a basic explanation of what your particular work of fiction expects me to accept, and I'm pretty likely to do so.
What I do have trouble with, however, is inconsistency. Tell me that there's a guy who can move faster than the eye can see, and has some funky ability so he doesn't burn up in the process...no problem. But then turn around and put him in a showdown with a single opponent who relies on a gun, which speedy should be able to take away before it can be fired - now we have a problem. This exact scenario has happened on CW's The Flash, which is a show I actually like quite a bit, but I had some trouble accepting that particular scene. The bigger the distance of the initial premise from reality, the more often you get this sort of inconsistency.
A well-crafted story can make things easier on the audience, by including believable reasons behind these kinds of scenarios. For instance, in that Flash-and-gun scenario, have the villain rig up the gun to explode or shoot randomly as soon as anyone else touches it. (Which is in fact what they did in a later episode.) While you probably couldn't do that in reality any more than a guy can run at light speed, having that added detail gives the viewer an excuse to believe in the scenario.
Most of the best fiction I've encountered requires suspension of disbelief just once, setting the initial scenario, and then everything follows logically from there. Harry Turtledove's various alternate history novels are a great example of this. The Guns of the South is perhaps the most famous; an alternate Civil War in which the Confederacy was given 20th century firearms. Once you get past the initial hurdle of accepting that premise, the rest of the story makes sense without forcing yourself to ignore logical holes.
By definition, fiction is going to contain something untrue, and much of the time it's something fantastic. The consumer is going to have to suspend their disbelief along the way. Really good fiction defines and explains those differences from reality in a way that the observer can understand and easily accept.