CodeAcademy has introduced courses for many popular services, including Youtube, Bitly and SoundCloud. The free online courses walk you through how you can post and retrieve data from these services through their APIs (aka. Application Programming Interfaces).
An API is just a way for your apps to access some of the functionality of one of these services, using the AppFurnace Code tab.
There are already a few examples of how to plug your apps into Parse, enabling you to store data from your apps online, and then fetch it back from the server. That example is as simple to include in your app as copying & pasting, but with a bit more knowledge about how Parse works, the possibilities are huge.
Integrating your app with a database could mean including High Score tables for games and quizzes, keeping Analytics of how people use your apps and what features they use the most, or even allowing users to share comments with each other whilst they use your app. Some of the AppFurnace users have discussed allowing people to track their GPS routes as they walk around, which could be stored in a database and retrieved later.
All of these things are possible with AppFurnace, and all they require is just a little bit of planning when it comes to organising your database with Parse, and some tweaking to the examples that are already in the Forums.
We look forward to seeing what you come up with.