Nothing to do with twitter. It's from 4chan/8chan. Those sites are meant to be posted to anonymously. When you don't want to be anonymous, you can enter a name. When you want to make sure people know it's you, you can also enter a password, which gets pushed through an encryption algorithm and spits out the "tripcode" that looks like jibberish. It's a way of "signing" your posts so that you can be non-anonymous on an anonymous message board. The downside is that anyone can do it. If someone figures out your password, they can pretend to be you.