Speaking without conviction is when you use too many phrases like "I think", "but I also may be full of shit", or "it is my opinion that" to qualify statements.
You could argue that preambling with these qualifying phrases is redundant. Any statement by a person obviously reflects what they think or believe, hence it is not necessary to add these phrases. Additionally, somebody believing something does not make something true, so it is not necessary to add a disclaimer stating this.
I remember once being criticized for speaking this way and being told that I would go farther in life if I just spoke like I believe every word I say. My problem with this is that I am not trying to sell something (most of the time).
I think maybe we should all use phrases like that more often, to remind every one every once in a while that our brains are not infallible and that we are not trying to sell each other stuff most of the time.