One of the key problems with the block system in core is it's very limiting. You are limited to a small set of tools for when and how to show a block. Once you lay out your blocks you are basically done—blocks can't be placed in multiple regions. Most importantly, block configurations are not exportable. With the Context module, you lay things out based on the context of your site. A block can exist in one region for one context and a different region for another. Essentially Context is a more advanced block placement form.
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This video covers a topic in Drupal 7 which may or may not be the version you're using. We're keeping this tutorial online as a courtesy to users of Drupal 7, but we consider it archived.