What Is An Outliner?
Briefly, an outliner is a tool you use to make lists, but that's really an oversimplification. An outline helps you organize information in a structured hierarchy, present it in a logical form, and show relationships between different items. An outliner is simply software that helps you to make outlines, helps you organize your thoughts, and helps you share them with other people as quickly and easily as is possible.
Things you might use OmniOutliner for:

To-Do Lists - Keep track of things that you need to do. Check tasks off when you complete them. Group related tasks. Gather completed tasks together under a new group so that you don't clutter your unfinished tasks. Add a column to record the date you completed the task.
Basic Project Tracking - Track tasks for a project just like a to-do list. Add columns for owner, due date, estimated time to complete, priority.
Writing - Create an outline in OmniOutliner, where you have a rich set of commands for manipulating the outline. When you're done export to Plain Text (with tabs), load this into a word processor, such as Word, and continue writing.
Track Your Work - Create a group called "Week of" with items for each day of the week. Copy this each week and update the group title with the date. As you accomplish tasks add them under the current day. When you go to your weekly staff meeting you'll have a list of what you did that week.
Decision Making - Have two columns, one for arguments for and the other for arguments against.
Taking Notes - During class, a meeting, or a talk at a conference.
Preparing For A Presentation - An outline is a great way to organize what you need to talk about.
Checklists - Use it as a checklist to make sure everything in a regular procedure is complete. For example make a checklist of the step required for a release of a product. Or Apple has a checklist of Human Interface Guidelines for creating Aqua applications. Create an OmniOutliner document out of that and use it for your application.
For Software Developers - You can view plist and strings files, as well as files generated by the sample command.
Manage Release Notes For Your Product - I use OmniOutliner to keep track of its release notes, and use the HTML exporting to add to the release notes on our web page.
Peer Pressure - All of your friends are using it and sending you OmniOutliner documents. You can view and print these even if you don't own an OmniOutliner license.

Related Topics
Table Of Contents: Getting Started
Terminology
The Document Window
Using OmniOutliner
Saving & Printing Your Outlines