To use Twitter anonymously, especially when one's motives depend on it.
I really want to tell so-and-so off, but I'll get in trouble. I'll just send him some vile insults incogtweeto.
When you tweet from a different account in order to hide your identity. Main reason is to keep hilarious yet potentially non-PC tweets not connected to your name.
Somebody went incogtweeto on my account last night and told @not_in_my_hair that i love giving blumpkins to horses.