A monolgue is is either a long speech by one person, a dramatic work for one performer or a scene within a longer piece where just one person speaks. I'm not sure if that means anyone who talks to themselves is a monologist whose monological habits cause them to monogolize from time to time, but I expect it's something like that.
I tried chatting to this chap, but that turned into a monologue.
Anyway, moving swiftly on ... If you've written a monologue, or fancy giving it a go, you might like to enter it in this competition.