means A focused beam of bright light aimed at a single performer or object on a stage, or by extension the concentrated public attention that falls on one person.

from A plain compound of "spot" and "light" — a light that lands on one spot rather than flooding the whole stage. "Spot" itself is an old Germanic word for a small mark or patch, related to Dutch and Low German cousins. The theatrical sense emerged with stage lighting, and the figurative "public attention" meaning followed naturally — once a beam could pin a person in brightness, so could the eyes of a crowd.