This in an interesting saying, and over the years has transformed. In it's original form, to throw down was to take something from a high place (like a leader, or tyrant, and remove that thing from it's high place.
Thanks to Hockey and the Philadelphia Flyers, the term throw down is synonamous with starting a fight, which leads to a beat down.

If you pronounce it with the silent-r, as in "th'ow down", then you're mimic(k)ing a piece of ancient b-boy lingo -- it can be the non-firearms equivalent of "bust a cap in yo' ass" ("...ah, when I were a lad, we used oor fists..."), or it can be something less violent, like a few rounds of hoop with some kids from another neighborhood ("we th'ew down Sunday on some crew f'om Hollis -- you shoulda seen my fly crossover when I...").