The word continuation comes from the late-14th century Old French word continuation, derived from the Latin continuationem, meaning "a following of one thing after another" from the verb continuare (to join together or make continuous).  It was comprised of com- (together) plus tenere (to hold). Literally, it means "holding things together" without a break.  

According to the Oxford English Dictionary (OED), the noun continuation was first used in English during the Middle English period (1150-1500).  It entered the English language around 1374 through translations by Geoffrey Chaucer.  According to the OED the word continue (as a verb) first appeared in English with the earliest recorded evidence dating from before 1340 in the religious and spiritual writings of the hermit and author Richard Rolle.  The noun continuity was first used in English in the mid-1500s (specifically recorded around 1543). 

Continuity (or continuation) in storytelling is the logical, consistent flow of plot, characters, and rules from one scene or part to the next. It matters because it protects the illusion of the real world, keeping the audience focused and trustful.  

Why Continuity (or Continuation) Matters:  
Builds Trust: Keeps the unwritten promise made to the reader or viewer that the world's rules will not randomly change.  
Prevents Confusion: Allows people to track action, time, and space smoothly without getting lost.  
Protects Immersion: Stops jarring errors (plot holes or sudden character changes) from pulling people out of the experience.  
Deepens Character Growth: Ensures that past trauma, choices, and lessons actually shape future actions.  

Key Parts of Story Continuity:  
Internal Logic: Magic systems, physics, and character abilities stay within established limits.  
Timeline and Space: Travel time, scars, clothing, and item locations match across scenes.  
Behavioral Consistency: People act in ways rooted in their established traits and past events.  

Just the facts:

CONTINUATION Definition & Meaning - Merriam-Webster

CONTINUATION Synonyms: 36 Similar and Opposite Words | Merriam-Webster Thesaurus

Continuity vs Continuation - What's the difference? | WikiDiff

CONTINUANCE Definition & Meaning - Merriam-Webster

Continuance vs. Continuation - Rephrasely

CONTINUOUS Definition & Meaning - Merriam-Webster

CONTINUE Definition & Meaning - Merriam-Webster

CONTINUED Definition & Meaning - Merriam-Webster