The white boxes on the map are discoverable items. If you tap the box, it tells you the name of the object. If you find all the objects on a map, you get a badge. If you get all the badges, you get a biscuit.
That's a lie. A dreadful, cruel lie. There are no biscuits.
Here, I've chosen the longer route, so I'll get to see the "collectible" illustration. You can choose which fork to take at any earlier point, but once you've reached it, it's locked and there's no going back.
Once you've unlocked a clip, you can play it at any time, even while you're tracking steps for a different episode. If you tap a clip, all the ones after it will play as well. Better yet, from the app's settings screen you can choose to be notified when clips unlock, or set them to play automatically as soon as they unlock, making the whole experience much more convenient.
The statistics-tracking page wasn't in the app when it was first released, was later added, then was taken out again for tweaking in Version 1.0.6. If it's in the app, you can find it on the same page as the activity summary. In Version 1.1.2 there's a new information page instead, which tells you, among other things, how many of the objects on the page you found.
Here's what it looks like when the app's running in the background. It'll also tell you if there's a "New activity" available, and after the February 10 update, it'll tell you the names of the audio clips you've unlocked recently. It also gave me a message saying I could touch the notification to see the activity summary of a completed episode, but touching it only took me to the app, not that particular summary. The devs are still tweaking this app, and the changes so far have been very good.
The first set of episodes ended in a satisfyingly dramatic way. Looking forward to Chapter 2!