Today it means: The transcription, either verbatim or in edited form, of the dialogue and sometimes sound effects of a program, displayed onscreen and synchronized with the program, most frequently used by the deaf and language learners. Closed captions are encoded invisibly, and displayed by a decoder. Full definition →
"Closed" originally indicated that such captions were by default not visible until activated (opened) by the viewer turning them on, in contrast to open captions which are embedded in the video itself, visible to all.
Etymology from Wiktionary, CC BY-SA 4.0.