The word "mesmerized" is derived from the 18th century physician Franz Anton Mesmer.  He developed a controversial theory called "mesmerism," which involved a mysterious force called "animal magnetism" that he believed could be used to cure illnesses and induce a trance-like state. The word "mesmerize" first meant "to subject to mesmerism," but later broadened to mean "to fascinate" or "to hypnotize". 

The first known use of the word "mesmerized" in English was in 1829. 

Examples of mesmerized used in a sentence: 
"But that day in 1996, the movie Twister mesmerized him."
"Check out the fierce glare of the bald eagles — the birds are mesmerizing." 
"As a child, she was mesmerized by the paint jobs, hydraulics, and the curves of the cars." 
"Always mesmerized by inner melodies and day-dreaming, on family camping trips he packed his score pad to compose and arrange."
"The child is unusually mesmerized by columns of ants on the ground and does not hear the calls."
"Pundarika is mesmerized by her beauty and gets into a relationship with her."