Subtext (noun) derives from the prefix sub- (under) and text, with roots in the Latin subtextere, meaning "to weave under".  

According to the Oxford English Dictionary (OED), the earliest known use of the noun subtest in English is from the 1880s, with the earliest evidence specifically dating to 1884 in the writing of J. A. Nettleton.  Other sources claim it appeared earlier (1726) in a literal sense to describe text printed below other text on a page, its usage in character analysis and acting theory originated from translations of Konstantin Stanislavsky's work.  The modern meaning of the term of "within a text or conversation gained prominence around this time, often associated with acting theories" appeared between 1945-1950.

Subtext in writing is the implicit, underlying meaning beneath dialogue, action, or description, often described as "reading between the lines".  It represents a character's true, often hidden, thoughts, emotions, or motivations, which differ from what they say or do directly, adding authenticity and tension. It is a powerful tool to "show, not tell," creating a richer, more complex narrative. 

Examples of Subtext in Writing: 
Dialogue/Direct Meaning vs. Intent: A character says "I'm fine" while slamming a door, suggesting anger, sadness, or a refusal to communicate, rather than contentment. 
Romantic Tension: Two characters engaged in witty banter or arguing, but the underlying message is "I love you" or "I am attracted to you". 
Hidden Agendas: A character offers a "generous" gift, but their underlying intent is to manipulate or buy loyalty. 
Metaphorical Description: In Kramer vs. Kramer, a character makes French toast while struggling to connect with their son, with the crumbling toast serving as a metaphor for their failing, chaotic life. 

How to Identify and Use Subtext:  
Focus on the "Unsaid": Look for what a character isn't saying but clearly feels or implies. 
Analyze Conflict: Examine scenes where characters' words contradict their body language, actions, or the situation. 
Use Action/Behavior: Replace emotional dialogue with actions that imply emotion (e.g., staring at an empty ring finger instead of saying "I'm lonely"). 
Create Ambiguity: Introduce nuance into dialogue to force the reader to infer meaning. 
Balance with Clarity: While essential, subtext should be balanced with direct moments for contrast, preventing the story from becoming too opaque. 

By utilizing subtext, authors can make scenes feel more realistic and compelling, drawing readers deeper into the characters' inner lives and motivations.