Biography
Knives as a primary weapon are rarely used by the most moral, upstanding, honorable types. There is a strong cultural association between knife-wielders and crime or treachery, and as such, those who use short blades as their weapon of choice are usually Combat Pragmatists and/or The Sneaky Guy.
This may be due to the properties of a knife: its small size and light weight mean that it doesn't encumber one's movements when sneaking around or fleeing a crime scene. This also allows it to easily be concealed on one's person, both before and after using it to stab someone: the revelation that someone has a knife hidden in their sleeve or boot can make for prime material for a Traitor Shot. However, these properties also make it less effective against a combatant who sees it coming, as its reach is short, and its small size makes it harder to inflict a fatal injury compared to a larger weapon like a sword. Therefore, the types who gravitate towards this weapon will rely on stealth, trickery, and agility to best take advantage of its strength and minimize its weaknesses.
Because Poison Is Evil, and knife-users aren't exactly nice guys, knives are a common choice for Poisoned Weapons. This can also help with the aforementioned difficulty dealing fatal damage: if the victim doesn't die from the stab, the toxin will finish the job. Ironically, this would be much less effective in real life than it is in fiction: as you know, being stabbed makes you bleed a lot, which makes it likely that the poison would just get washed away by all the gushing blood.
Daggers, in particular, are a popular choice for guile characters due to their long history of being used to carry out assassinations, which gives them the reputation of being a "dishonorable" weapon. The dagger's narrow blade and acute point are specifically designed for piercing vital organs and give them few utilitarian purposes like an ordinary knife does also lends to this reputation; a character packing a dagger or stiletto isn't likely to be using it mainly to cook, hunt, or defend themselves. The expression "cloak and dagger" refers to secretive and underhanded activity. This comes from both In the Hood and the association of daggers with being easily concealed weapons that might come in handy during a sudden betrayal.
Despite this, such characters are not inherently evil or antagonistic. A Lovable Rogue on the heroes' side can use a knife to represent the "rogue" side of the trope without diminishing the "lovable" aspect. That said, they will usually be an Anti-Hero at the nicest, since sneakiness and pragmatism are not the traits of an Ideal Hero.
In fiction, knife-wielders will often be thieves, assassins, spies, or Ninjas. In gaming, their playstyle will commonly be that of a Fragile Speedster, Stealth Expert, and/or Critical Hit Class and are usually better able to use the Back Stab mechanic to deal extra damage (the ability to Back Stab may even be exclusive to knife users).
While the term "dagger" specifically refers to double-edged knives, note single-edged knives can also carry the same sneaky connotations. The trope name uses "dagger" because we like the Alliterative Name, not to restrict which knife-wielders fit the trope.
See also Retractable Weapon and Hidden Weapons for particular properties of certain knives that help them be concealable. The Sinister Switchblade is a sister trope more commonly used outside of period/fantasy settings, and usually implies a lot of the same things about the character wielding it.
These type characters are often Blade Enthusiasts.
For psychotic or unhinged characters who wield knives, see Psycho Knife Nut.