What problems do outliners solve?
Outlining is a process of viewing and manipulating a structural view of a piece of writing. This is done by taking advantage of the tree-like hierarchy that naturally emerges in writing as defined by the paragraphs, sequences and sections.
Any piece of writing exists at multiple levels of resolution. There is the selection of the word, the crafting of the sentence, the sequencing of sentences into paragraphs, the sequencing of paragraphs (possibly into sections) and the piece as a whole 1. The piece needs to work on all of these levels for it to be a good piece, so the piece must be analyzed at each of these levels as well as its coherence as a whole.
The conventional model of digital word processing is to view the text as we would an analog piece of text: as one continuous document. This one-dimensional view places a burden on our ability to navigate through the piece, analyse one section while keeping another one in mind and taking multiple higher levels into account simultaneously. This is important considering writing is a highly non-linear, recursive activity, where you can expect to cycle through research, note taking, structuring, drafting and editing — all of which may require information to be captured, displayed and dissected in distinct ways.
Because outliners are built on a different model, one where the text is treated as a tree-like hierarchy — which you can navigate, collapse and expand, as well as modify — it becomes much easier to make your way through the document and analyse and make modifications at different levels of resolution. Put simply, you can work on a specific section in isolation to get it right, whereafter you can switch back to an overview of the entire piece to make sure it flows smoothly.
Because of the inherent complexity of the writing process it helps to have a plan and an outline can be that plan. A plan reminds you where you want to go, and what needs to be included, but often you'll also discover new things along the way that need to be included. For this reason, it's important the plan to be updated easily. A digital outline will typically offer this ability.