I find that the low speed and physical difficulty of writing helps me focus my thought process. There are no toolbars of formatting buttons demanding they be used too. If I recall something and go off on a tangent, drawing an arrow to the breakoff point for later reconsideration is natural and effortless. Paper also works better than just thinking and memorising because with that I tend to think in circles, constantly re-analysing what I'm already comfortable with. Paper forces closing a line of thought and moving on.
This blog post, oddly enough, was written and posted from a mobile phone, as has been pretty much every post I've made in the past year or so.