For me at least, it was just something that I built up over time. At first I mostly just presented my character as myself myself but as an owl. Over time, as I interacted with others on the forum and elsewhere, I started to build a unique character based on random fragments of RP.
For instance, the whole idea that I am the CEO of a global mega corporation started off by pure chance. It was Friday at the office I work at and that's when we have donuts. I mentioned that on the thread and, instead of giving my company's real name, I use the moniker of Birb Inc. That one bit of improve started this idea that I was an employee at a bird related office building. But even then, the idea wasn't all there. At first I thought of my character as just a low level grunt at Birb Inc. Over time I changed that to being the CEO, I swapped the normal office for a mega corporation, and I altered the name of the company to the ominous Birb Consumer Products (because Robocop).
I started off as just some office grunt and now I'm basically a super villian.
A little bit of improve can balloon into a full fledged idea