Bitly is a url shortening service. Building a url shortener is a common interview question / take home project, because it's a minimal project that involves many aspects of web development. Build a website that allows you to submit a link, then gives you a new, hopefully shorter url to use for that link.
Typically at Hacker School understanding is emphasized over ability to throw things together - this is an exercise in the latter. It's also practice reading documentation to figure out how to do things quickly, and a guided way to gain exposure to web development concepts that you might research more after this sprint today. It reminds me (in good and bad ways) of a hackathon.