A little back story: Through my teens I was an ardent fan of films and sci-fi (primarily Star Wars), and Star Trek always piqued my interest, but I was too intimidated to invest the time to acquaint myself with a franchise that stretched over television and film since the 1960s.
That being said, I came across this episode while scanning TV channels and was immediately drawn to the character of Data, an singular android who dedicates his improbable existence to evolve and grow in order to be more "human." His quest in this episode included creating a new android in the hopes of improving upon his own limitations through his designated "offspring" (as most true parents do), including having this android eventually find a way to develop authentic emotional reactions.
However, when Starfleet grows impatient with the development of Data's new android, they threaten to confiscate it, instigating a surprisingly emotional struggle over the philosophy of sentient rights and acceptance that ultimately becomes overshadowed in the face of tragedy. It's all the more astonishing to consider the most emotionally devastating moments of the episode feature characters who can't project any emotions at all.
Brilliantly written, performed, and directed, this is one of the finest hours of television that succeeded in appealing to an outsider of the franchise and making them a fan for life.