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It means that anyone can run their own REST API for Bitshares, simplifying interaction with python-bitshares and establishing an alternative software stack to BPAP.

With this, you could query BTS network stats for website widgets, charts, scripts, data mining, etc.

wonderful, thank you. Is this simliar to how Steem already works? Does Steem already allow this? Is this why services like SteemWorld can exist?

This API doesn't exist for Steem yet, however it uses the same Graphene toolkit (albeit tweaked), so it's entirely possible to make a similar HUG REST API for Steem.

I'd probably use: https://github.com/xeroc/piston-lib