The level of formality in language, from casual slang to elevated literary prose, chosen to fit the situation.
Register is the degree of formality in how someone uses language. You instinctively shift register all the time - you don't text your best friend the same way you'd write a cover letter. In fiction, register applies to both the narrative prose and individual characters' speech. A character's register reveals their education, social class, comfort level, and relationship to whoever they're talking to.
Register is one of the fastest ways to characterize someone on the page. A character who says "I require your assistance" versus "Hey, can you help me out?" is telling the reader volumes about who they are without a single line of description. Mismatched register is also one of the quickest ways to break a reader's immersion - if your medieval knight suddenly sounds like a modern teenager, you've lost them.
The entire plot revolves around register. Eliza Doolittle's transformation from Cockney flower girl to apparent high-society lady is accomplished purely through changing how she speaks.
Mattie Ross narrates in a formal, almost legalistic register that's wildly at odds with the violent frontier action. The contrast is both funny and deeply characterizing.
Welsh writes in Scots dialect and casual register throughout, creating an immersive authenticity that would be impossible in formal standard English.
A professor, a teenager, and a plumber should not sound identical. Vary register between characters based on who they are and who they're talking to.
Real people adjust their register constantly. A teenager talks differently to their best friend than to their principal. Let your characters code-switch.
An action thriller narrated in elevated, formal register will feel sluggish. A literary meditation in casual register may lack weight. Match your narrative register to your story's needs.
Write a scene where a character receives bad news in a professional setting, then immediately calls their best friend to talk about it. Write both conversations in full. Pay attention to how the character's vocabulary, sentence structure, and emotional expression shift between the two contexts. That shift is register in action.