(CONT'D)

The cue extension marking that a character's speech continues across an interruption or page break.

(CONT'D) after a character cue means the same character is still talking — their speech was interrupted by an action line or a page break and now resumes. It cues the actor that this is one continuing thought, not a new speech.

It's bookkeeping, not writing: professional tools derive it automatically as lines move, which is the only sane approach — hand-maintained (CONT'D)s go stale on the first edit.

Go deeper: Screenplay Formatting Basics