I do consulting for Podio so I've seen a million different use cases. I use it to manage my whole business (client management, job/task tracking, billing w/ integration to accounting software).
Most commonly, I see it being used for CRM, Project Management, and randomly there are a lot of real estate businesses using it for things like property management and house flipping. A lot of people coming in were only using Excel previously, and pretty much anything you can store in a spreadsheet, you can create as a Podio app and organize/collaborate way better.
With Podio you're basically getting custom software for not-custom-software pricing. You can do just about anything with it which is why it can feel a little directionless when you're first getting started. You can start with some app packs in the app market, usually I find they are a bit bloated but it's a good starting point for beginners to give you an idea of what's possible:
The huge key is the automation component - this is what sets Podio apart from anything else on the market that I've seen. You can automate anything, including setting up integrations to outside systems (kind of like how you might do with Zapier, but with way more functionality).