Android applications are structured like web pages, even when you look at them from a developer's perspective. Besides other things, each app consists of a number of activities. An activity is the UI you see on the screen, and there's a separate activity for each piece of UI you see in an app. For example, your Twitter app might consist of an activity for the timeline, another one for sending a new tweet, another one for setting preferences, etc. It helps to think of an activity as a web page and an app as a website consisting of a number of web pages.
When you're in AppX and want to open a document/URL in AppY, you send AppY an intent, which is a fancy word for message. Android then replaces the current activity from AppX with a new activity from AppY. But that's not all. You can directly send an intent to an activity in AppY, or you can send an intent to AppY and let it decide which activity to use for handling it. You can even just broadcast the intent and let Android decide what to do with it.
So, in reality, you're not using "apps" at all. Instead, you're using a hyperlinked collection of activities, each of which just happens to belong to a collection of activities called an app. When you look at it this way, it's just natural that Android has a home button and a back button. Both those buttons work in natural, predictable ways. If I open an unread text message from my home screen and then hit the back button, I'm back at the home screen. If I open my inbox in the messaging app, navigate to the unread text message and hit back, I'm back at my inbox. What could be more natural?
(Also, IMO, the Android API and developer tools make Cocoa and Xcode look like toys. It's like comparing DirectX with BGI.)
Talking of usability: in my experience, Android is far more usable than iOS. It might not be pretty, but it manages to get nearly everything right UI-wise. Less buttons on the phone != better usability. What if your laptop had only the 26 letters and every other function was bound to a double-tap or press-and-hold action? Double tap Q for F1, press and hold M for backspace?
Because as part of the original design, iOS had no particular place to go back to other than the home screen...hence the singular home button...which actually is a global back button of sorts.