Basic Page inherits Common.LayoutAwarePage. This gives your page various capabilities like the automatic back button and a visualstatemanager for snapping among other things.
Blank Page only inherits Page and does not get any of the above capabilities. So for example if you need to incorporate snapped view in your page, you need to add a handler for the size changed event in your code.
A Basic Page makes it very easy to just write all the snapped changes in your VisualStateManager in XAML and then test it without running your code using just the device tab where you can select state of your device.
The MainPage in your project is a Blank Page and I prefer to create all other pages as Basic Pages to not worry about stuff like the back button.
That being said, Windows 8.1 apps do not include the LayoutAwarePage so if you are not used to the LayoutAwarePage, do not bother.
Let me know if you need more clarification.