Paper is great for thinking because it doesn't distract you or interrupt you.
Also, if I'm working on a project and can't figure out which of a dozen possible things to do next, I write down lists of tasks. These will eventually get transferred to digital form, but I find that circling important things and drawing arrows between them is a lot quicker on paper than messing around with some user interface on a computer, and this lack of friction promotes a state of flow.[1] If I get bogged down with data entry, it's easier to forget an item that came up while writing down another item.