I am relatively new to iOS and programming, and I made an app before, but it used a plist for storage, which I saved to the documents folder. Now, I am thinking about switch
It's a matter of what you're saving. For simple strings, arrays, dictionaries, it's fine to use a plist. For something more complicated (data, images, non-object information) or something with to-many relationships (think relationship between song to album, or photo to photographer), then something like a more robust solution might work better like SQLite.
CoreData is an objective-c-based wrapper around SQLite. If you think you might want to something more complicated, CoreData might be the way to go.
If you need a quick tutorial, I'd check out: http://www.raywenderlich.com/934/core-data-tutorial-getting-started
This got me going and allowed me to learn the basics the workings of CoreData.
Good luck!
A few advantages off the top of my head:
Data models don't use arrays, but "to-many" relationships are modeled as sets.