There are many conventions that appear repeatedly in the genre of horror movies. These are things which are so imbedded in the nature of horror that they are not just expected, but a fundamental part of it. Clichés and concepts that are so common as to be universal. Things like abandoned buildings, dark nights, mysterious sounds… and knives.
Yes, as scary as monsters, aliens, demons and assorted over horrors may be, sometimes the truly scariest thing the protagonist of a horror work is confronted with is a maniac with a knife- and in some ways it is far worse than any otherworldly terror could ever be without the best kitchen knives under $100.
One might think otherwise, given the other examples do have their own strengths- be it a far-reaching impact, like aliens invading the planet, inexplicable origins and utterly incomprehensible motivations, as some otherworldly entities could have, and a wide variety of possible concepts that can go hand in hand with inhuman entities. However, in spite of all that, there is one thing that your simple knife wielder has that they do not.
What they have that makes them truly terrifying is familiarity, or, to put it another way, reality. While we may be scared of horror monsters for the duration of a movie or book, they are confined in the story. Maybe we will go back to them later when we want to be scared again. But there are humans all around you, as a member of society.
Break-ins do happen, all the time. So do murders and attacks. The fact of the matters, your knife-holding killer is someone we genuinely are afraid of, because they are someone we very well could meet. They are the reason we lock out doors, the reason we keep a light on when we sleep, to fool the murderers we fear are lurking outside into leaving us alone. After all, if there is a light on, they’ll think we’re awake, and they won’t come.
It’s the same line of thought behind the existence of nightlights, only applied to something real. Children may use the light to keep nightmares away, but adults use it to keep the real terrors at bay. And it is a terror that could appear at anytime. That is the real reason for fear, after all- the notion that what is happening is terrifying, that we can, in some way, grasp the horror of what is happening. And in this case that horror is something so plain and ordinary that it can actually happen, right in our homes, in any place.
All that said, aside from domestic terror, there is certain connotations by featuring a knife wielding character. Weapons, after all, do pick up certain associations over time. Katanas are mostly used by samurai or ninja, cutlasses by pirates, and so on. Similarly, survival knives and especially knives are featured as the weapon of psychopaths and serial murderers in many stories and movies especially. It has gotten to the point where, if a character uses the weapon, they then carry the assumption that they fall into that criteria.
To put it more simply, if a character is often seen with a knife and they do not have it for an already established reason, then it very well could be assumed they have one because they want to hurt someone with it. It’s often a joke, even, that’s how prevalent it is. In fact, even if one does have a good reason to be carrying a knife, they are often portrayed as someone eager to use it, or violence in general.
Rather than the knife being used by someone violent, it appears that the knife is a violent weapon, and if someone has one they must be violent. This is, of course, a false connection; there’s no reason for a character with a knife to necessarily be any more violent than one who does not have one, but by people thinking that it is the case, it often becomes so in future stories and writings as the ones writing try to appeal to this concept.