To be brash is to be rash – b rash indeed. It’s to be flashy and crashy and probably trashy, perhaps to be brutal and break things. It is to say to your brain “sh!” before it can finish. The Oxford English Dictionary definition of the adjective brash is “Hasty, rash, impetuous; (orig. U.S.), impulsive, assertive, impudent; crude, insensitive; flashy.” Ashes to ashes, but bashes to the brashest. It is a characteristic most especially of the young, and in particular of young men. Words it most often shows up with, according to the Corpus of Contemporary American English, include (in descending order) young, loud, style, bold, cocky, and arrogant.
Here’s another word you may see with it: water. As in water brash. This is a medical term. It’s not brash water; here, brash is a noun. A more technical term is reflux. You lie down, the acidic contents of your stomach – including excess saliva – flow up, it produces a burning sensation and a sense of unpleasant water flowing back into your mouth and probably some general gastric discomfort. So it’s water and it’s rather brash. But this is the noun, meaning ‘break, attack, assault, burst’. It’s the original brash.
In fact, brash the noun was around since the 1500s, while brash the adjective has only been around since the 1800s. It’s quite the brash upstart. But wait, there’s more: there are actually two each of noun, adjective, and verb for brash in the OED. The other noun version is ‘heap of fragments, such as rock rubble or crushed ice’. The other adjective version is ‘fragile; brittle’ and mainly applies to timber. The two verbs are an obsolete one meaning ‘assault, attack’ and a 20th-century one meaning ‘remove the lower branches of a tree’. They don’t all have identical origins as far as we can tell, but we can’t entirely tell for sure either. The main thing is that the sense we commonly use, like a couple of the others, seems to have imitative or sound symbolic origins – that is, it makes use of the phonaesthemes /br/ (as in break, brunt, brittle) and /æʃ/ (as in smash, crash, dash, splash). They were grabbed and rashly bashed together. But the result seems to hold water.