In which I kvetch far too much.
To not get with mincing words, Shiki's eyesight allows him to see death in almost all things. This death appears in spiderweb-like lines and quarter-to-baseball sized dots that cross and cover everything--mineral, animal, plant, space, etc. Technically, the lines of fated end encompass EVERYTHING, but what Shiki will see is decidedly up to his level of comprehension, as well as his level of stress. So long as Shiki can understand the "concept" of death in an entity or object, the lines and dots will appear. We'll dive further into that in a minute.
How he can "kill" the object is by taking an edged object (canon varies on this. Anything from the fineness of a wire to the dull part of safety scissors. I'll just assume a basic wedge is all that is required) and trace the lines. The object will break along the traced path. Because it is the concept natural end that Shiki is tracing, things like augmented or assisted defenses are typically ignored (Spoiler Example: Ciel's immortality is a direct result of the Dead Apostle known as Roa being alive. So long as he remains alive, time itself will always reverse any injury Ciel gains, making her fully-immortal. However, Shiki can still verymuch kill her by tracing her lines--we'll go into the why in a moment).
There has been a lot of discussion about how the Mystic Eyes operate to ignore special defenses, but from interviews from Nasu, I've concluded that the Eyes actually see the absolute future of all things, similar to if Shiki was seeing the clock over someone's head, ticking away their life. Tracing the lines shorten's that object or entities time, and stabbing the points brings that object or entity to its immediate end. So, so long as that particular set of circumstances is met (The object exists in a reality-bound timeline, Shiki can "conceptualize" that object or entity's time), he will see the dots and lines.
And now for the penalties, and believe me, they are massive (hence why he's not as godmoddy at all). For all that amazing power (The eyes are a psychic ability, so they're undetectible unless that person is digging in Shiki's head), the Eyes are a huge strain to Shiki's health. Typically, he'll geat headaches to heavy migraines from looking at lines for too long. He actively risks becoming a vegetable if he is forcing himself to see the lines on an object or entity. Arcuied has times of the day when she's weak--this is how Shiki was able to cut her up, initially. But other times, she's nigh unkillable because he has to focus incredibly hard to see the lines (he almost permanently blinds himself in one of the endings of the game from overstress. His target was a poison running through someone's system). Another point is, despite being able to see these lines and points, Shiki still has to be able cut them with his own hands. While he's fast, he's certainly not the fastest in his canon (truth be told, everyone else has less penalties than he does). The biggest point of all, of course, is Shiki values and respects life far too much to go on homicidal killing sprees. So you'd have to be doing something pretty damn bad in order for him to take off his glasses in the first place.
WHAT DOES THIS MEAN TO YOUR CHARACTERS?
Next to nil unless it's a bossfight in progress. I'm putting this out because folks like reading about this stuff. I mean, sure he could kill all but a handful of people in camp, but then who would make lunch for him? ;;
There is a natural pecking order of the supernatural in the Nasuworld: Shinso (True Ancestors), Demons, Dead Apostles, and the like prey on humans. Psychics prey on them in turn. Hybrids prey on psychics. The Church preys on everyone. The Magic Guild preys on the common sense of the universe (I love Zeltrech, but let's be honest--the Holy Grail War was a very stupid idea).
In this pecking order, there was a clan of utter badass psychics that did a lot of demon-killing. They were the Nanaya. They were powerful because despite being human (read: COMPLETELY inferior to demons/shinso/etc), they had natural ways to topple such entities. This power of theirs was achieved through years of inbreeding and honing of fighting skills (Motherfucking: sure it's awkward, but you can't beat the post-coital cuddling), and they were prominent as badass demon-killing clan number one.
Shiki is actually a blood member of this clan. And the last of his clan. As to why, recall the sentence about hybrids preying on psychics. Hybrids are humans that have contracted pacts for some insane reason to demons, reinforcing their downlines and unknowingly promising most of that same line will die from madness-related issues. They fool psychics because they have the ability to hide their demonic aura, letting them hide in plain sight.
Diving further will be a post best left for later, so let's get to what this means to Shiki. Despite his frail constitution and lack of physical activity, Shiki is technically in better health than most olympic athletes. His bloodline is strong, yo. He is capable of movement and acrobatics most humans can't do, and he does them at subsonic speeds. This is all dependent on one thing: his instincts.
His spider-sense reacts directly to imminent danger and inhuman presences. For the former, he'll quickly throw himself out of harm's way. For the later, his blood will come into play and he'll parry, block, and dodge until he can find and exploit a critical hole in his opponent's defense--a fatal occurrence when you throw the Mystic Eyes of Death Perception into the equation.
This doesn't make him Superman, however. While Shiki WAS trained by his biological father to use those instincts in a fighting style, his training wasn't complete. Worse, Makihisa mind-crushed the poor boy after his tragic accident when he was nine. So all he can remember and act upon are the warnings that let him know he's about to lose a limb/his life and that something should be done about it with all due haste. Except even THAT is not enough, sometimes (See: Ciel's route, Kohaku's route).
What it DOES mean for people of the not-human variety is that Shiki will boggle around you for the briefest of moments. He might also get headaches, and possibly bleed on himself (his scar does this neat trick when he's traumatized. Ruins all kinds of shirts. :<).