Most of the apps available in the App Store were written to be used on the 3.5-inch screens of the iPhone and iPod touch. When those apps were created, the iPad didn't exist, so the developers didn't know that one day they'd have to consider a 9.7-inch screen for their apps to run on (though, there are now iPad-specific apps. Learn how to identify them here).
Luckily, Apple thought of that when developing the iPad and added a feature that allows apps written for the iPhone to be resized to fit the iPad's larger screen. Apps resized this way are running in fullscreen mode.
Fullscreen mode on non-native apps is achieved by the iPad scaling the app's graphics ups (essentially copying similar pixels to make the image bigger). While that's not a requirement (apps can also run in an iPhone-sized window), it makes many apps look better.
To apps in fullscreen mode on the iPad, simply launch the app you want to use. If it's not native, it will appear in an iPhone-sized window in the center of the screen. At the bottom right corner of the window is a button labeled "2X". Tap it to change the app to fullscreen mode.
If you want to change it back, simply tap the button - now labeled "1X" - again.