In the first appoximation you can use org-mode the same way you'd use markdown -- merely for the syntax. But indeed, it shines when you use it within Emacs because you can extend it. Even the 'vanilla' setup is very powerful -- you get the markup, datetimes, todos, scheduling, agenda, clocking, literate programming, etc.

Spreadsheets.. personally, never had the need to use formulas, but they are very nice when you need.. well, to organize information in tables. For example, I'm using it with org-capture to track sleep data straight into the table, which results in a table row for each day (with an auto-generated timestamp).