The word "engrossed" traces its roots back to the Old French word "en gros," meaning "in bulk" or "in quantity," which came from the medieval Latin word "in grosso" meaning "Wholesale."   Engrossed may have also evolved from the the Anglo-Norman verb "engrosser," which meant to write in large letter or to draft something in its final form, and that came from medieval Latin ingrossare, which meant to thicken or write in a large, thick script.  The term evolved to signify complete absorption or deep focus on something, capturing the entire attention.  

The earliest known use of the verb engross is in the Middle English period (1150—1500).  The OED's earliest evidence for engross is from Middle English before 1400.  The adjective "engrossed" was first used in English in the late 1500s. The Oxford English Dictionary cites John Banister, a surgeon, as the first known user in 1578. 

Examples of the word "engrossed" used in a sentence: 
"I was completely engrossed in the book I was reading." 
"The leader asked his question with an engrossed expression on his face." 
"But such things were impossible when he saw her engrossed in a daydream."
"The members of the "rules committee" seemed to be engrossed in conversation."  
"The pair were so engrossed in their carnal activities that they did not even notice Loren." 
"She nods a curt reply as she is deeply engrossed in letting the sun's rays bathe her pale, freckly body." 
"His eyes opened slightly, unseeing, totally engrossed by the concentration required of him.

Just the facts:

ENGROSS Definition & Meaning - Merriam-Webster

ENGROSSED Synonyms: 67 Similar and Opposite Words | Merriam-Webster Thesaurus