How can I assign a block to a panel or mini-panel? I was reading the project description for Panels, and I noticed it was a way—using mini-panels—for me to rearrange the contents of my site.

So I just created a mini-panel with a two column layout. I want to add one block to the left and one block to the right. How can I do this?
Mini panels are blocks and you can add Mini Panels to Panels. You can't add blocks themselves to Panels, but usually most of the content that you can display in a block, you can actually display in Panels, content such as Activities, Menus, Mini panels themselves, Miscellaneous, Pages elements, Views, Widgets, Nodes, Custom content and more.

See Drupal - Blocks vs Context vs Panels.