I came across the phrase Drop Dead Gorgeous which means very gorgeous or good-looking.
Why does the above phrase have this meaning? How do the given words relate to the meaning?
Drop dead works as an intensifier in this phrase. The reference to death isn't literal; it's a hyperbolic expression meant to emphasize how incredibly stunning the speaker finds the person being described.
It's thematically akin to phrases like "I am so [adjective] I could die" (common examples: "hungry," "happy") or "I'm bored to death."
A first degree paraphrase of:
This person is drop dead gorgeous.
This person is so gorgeous that I could drop dead.
That is, "drop dead" is a description of the reaction of onlookers: they could drop dead due to the shock of seeing such a gorgeous person.
There are other similar expressions in English: shockingly, stunningly, and they are all tied to physical reactions that onlookers could experience (and display).
Imagine a teenage popstar walking down a mall, and the ripples it would create in the crowd: