Keep track of all TODOs in one's life. You can create TODO items and schedule them. You tag them (similar to hashtags) too. Now, if I want to see the list to things to be done today (or any day for that matter), Org Mode will generate the agenda for you. You can filter your agenda/TODOs - for example, if you are getting into a call with Team X, you can filter with "teamx" to get the list of items marked against the team. You can of course add checklists under tasks (sub items), and notes too. Recurring schedule is supported.
Keeping notes. Org Mode doubles up as an Outliner. You can keep hierarchical notes in a single large file. You can mix-in tables (with support for LISP formulae) for tabular data. You can embed images and LaTeX too. You can convert your notes to HTML or Markdown in a jiffy. There are shortcuts for instant note taking. You can archive sections that are no longer required.
I have stopped using mindmaps and now rather rely on Org. It can handle tree-structured information very well.
As a calendar. You can also add diary-remind reminders. Remember one's wedding anniversary (and Spouse's birthday) to save one's marriage.
As with everything in Emacs, configurable and extensible (with ELisp). Almost every method and every variable is Global. This is of course crazy, but the power that this proffers is enormous.
I learn something new about Org Mode every now and then. I do not consider myself as a power user, as I am sure there is still much left to be explored.
Good summary. One thing to note about org is it's not opinionated. Even the word "Todo" is up to you, in fact you can just tell it a bunch of "not done" keywords and a bunch of "done" ones. Over the years I've tweaked these. For example I use STARTED for tasks that I've begun but not yet finished, because I hate starting things but but not finishing them. I've set my agenda views to display these right at the top. Similarly I've added more resolutions like DELEGATED.
This flexibility means you can bend it to rather odd requirements. For example, in my current job I'm required to track time against project codes, but I have to scale the proportion against the hours I'm contracted for (it's a tax thing, I'm told). Org supports clocking in/out of things. It doesn't know what those things are, they are just items in the outline. So I structure my todos under the project codes then track time against those tasks or just directly to the project. Then I have an agenda view which shows me totals for each project and a column scaling the proportions to the total contracted hours over the period.
But you might have completely different requirements. You might want a flat backlog and to "refile" tasks into "sprints" when they get properly defined then set a deadline on the whole sprint. Org supports it all because it doesn't really care that much. Seeing people struggle with the likes of Jira becomes rather comical.
You might also like the org-babel features of creating executable code-blocks. You can even mix languages by using the output of one block as the input to another. Welcome to the future of 2012 ;)
I made one such document a while back with mostly Clojure, if you want to have a look: https://github.com/dnv-opensource/reagent-flow/
Org mode is a bit of a mystery to me thus far, collapsible sections are great but could you expand on what is so helpful to you and how you use it?