Once out, and once I've forced myself to represent the idea in prose or some other kind of model, I usually find that I've teased out detail in some areas that were previously woolly. I can begin to challenge the idea, to see patterns and gaps between it and the other ideas, to search the space around it and see further ideas, perhaps better ideas.
Once out, I feel like I have freed up some brain room for more thoughts. I don't have to maintain the cloud of things that the idea was when it was only in mind and I was repeatedly running over it to keep it alive, to remember it.
Once out, once I've nailed it down that first time, I have a better idea of how to explain it to someone else. So I can choose to share the idea and get the benefits of others' challenges to it.
Don't get me wrong, I do a lot of thinking in my head. But pulling an idea out, even to somewhere only visible to me, is a commitment to the idea of the idea - which doesn't mean that I think it's a good idea; just that it's worth exploring.