"A villain is traditionally the antagonist (main character's main enemy), although some have done wonders with, as you have said, a protagonist (main character) "villain"- that is, a villainous lifestyle as a career, most often in the comic book-superhero sense. By this I mean that the villain lives in a world chock-full of do-gooders in tights and underwear that may or may not have "superpowers" and who traipse around foiling these so-called villains' evil schemes, which usually involve world domination, revenge, murder, money, attention-bringing misdemeanors, and the like. The villains sometimes wear the bright capes-and-underwear themselves, and sometimes have superpowers (which is one of the most-used definitions of "supervillain") and almost always have some sort of doomsday machine or what-have-you used to accomplish their goals, especially if said villain is a Mad Scientist. They may or may not carry menacing death/stun/freeze/etc. rays to ward off heroes and heroines, which they usually regard as enemies. They sometimes have archnemesis-es or archenemies, who are usually "heroes" as well. They usually have an interesting backstory, which, if used to the extreme, can degrade the villain to merely "misunderstood". Some "villains" become such because, for one reason or another, society has dubbed them this and they eventually, willingly or unwillingly, begin to act out their part.
"Other types of villains can be much less extreme, and can range from a grumpy neighbor to a sadistic boss at work. These types of villains are the types the protagonist might encounter day-to-day, and mostly act legally (unless the protagonist or his/her allies are policemen, detectives, or other law-enforcers). The protagonist usually has to battle them, whether literally or figuratively.
"If you want to create a villain, give him/her an identity. Add quirks (from strange costumes and villain names to a dislike for cumin), weaknesses if need be (afraid of mice? That could be useful if the protagonist has access to a pet rodent), goals and aspirations (take over the world or become head cheerleader?), motivations (why are they doing what they're doing?), and, perhaps most importantly, the reason why the audience/hero should dislike or be pitted against them. Is the villain working for a big corporation that cuts down the rainforests and your hero is a faithful, picketing ecologist? Or does your hero want the position the sadistic villain holds? Give us a reason to love to hate the villain."
"Other types of villains can be much less extreme, and can range from a grumpy neighbor to a sadistic boss at work. These types of villains are the types the protagonist might encounter day-to-day, and mostly act legally (unless the protagonist or his/her allies are policemen, detectives, or other law-enforcers). The protagonist usually has to battle them, whether literally or figuratively.
"If you want to create a villain, give him/her an identity. Add quirks (from strange costumes and villain names to a dislike for cumin), weaknesses if need be (afraid of mice? That could be useful if the protagonist has access to a pet rodent), goals and aspirations (take over the world or become head cheerleader?), motivations (why are they doing what they're doing?), and, perhaps most importantly, the reason why the audience/hero should dislike or be pitted against them. Is the villain working for a big corporation that cuts down the rainforests and your hero is a faithful, picketing ecologist? Or does your hero want the position the sadistic villain holds? Give us a reason to love to hate the villain."