Difference between Parse and Core Data

Core Data and Parse often go hand-in-hand. Core Data is a way to save data to the device for use later - basically a database that is unique to your app. The data will persist across application launches though, which is really nice. Core Data lets you store almost anything - you just have to give it a schema for the kind of data you want it to store, and Core Data will store it. The downside is that because it's so flexible, it takes a lot of configuration. Take a look at this tutorial for a great overview of Core Data and how to get it up and running (it should still work even though it's for iOS 5). The general idea, though, is that, like a database, you can create records, fetch records, update records, and delete records stored on the device.

Parse, on the other hand, is a BaaS, or backend-as-a-service. It provides a server for your app to talk to, which means that you can have a central "repository" of data for all your users, or send data between different users, among other cool things.

One way you could use both Core Data and Parse hand in hand for the app idea you're describing is you have all of the places the user could ever possibly favorite on Parse (and your app fetches them whenever it needs them). Then, when a user favorites a location, your app stores it locally on the device in Core Data and marks it as a favorite. That way a user can view his or her favorite places even when they don't have an internet connection!

P.S. apparently on Android, Parse takes care of basic local storage for you! They say they're working on an implementation of it for iOS :)