I've read the website and all the comments and I'm still totally lost. Guess that means I'm not the target audience? To me a "music drop" is when someone releases a highly anticipated new song.
Lifelong musician - I thought from the title that it meant dropping a track on spotify at a specific release time. (I imagined, like, putting out one song from a new album at midnight every night). Most people I know would call this a "break", as in the build-up to where the beat breaks. Probably a generational thing.
Also lifelong musician and knew immediately what it meant. "The drop" is fundamentally different but not unrelated to a break - indeed typically it's after a break.
("break" and "breakbeat" are also overloaded terms, particularly in electronic music)
The (beat) "drop" is genre term for a buildup of tension, sharp pause, and then suddenly resuming at greater intensity/tempo. Usually associated with EDM/dubstep.
E.g. https://www.youtube.com/watch?v=db5f-A-vSyw (drop at 0:45 seconds in the video, thought the countdown to New years that takes up most of the stage should make that obvious anyway)....
Thought it's certainly not a new thing - plenty of classical music has similar moments, e.g. the 3rd movement to Beethoven's 5th symphony: https://youtu.be/xAQFJ1YpFaI?t=279 ("drop" at 5:05 when the horns blast their way in...)