As daffy says, most devices have a software operating system that runs them. Without an operating system most devices could do nothing.
Most of us know Windows from our PCs.
Often on phones the operating system is "hidden" (or it was till a few years ago). It is what provides the menus and icons and "manages" the phone.
The iPhone runs an operating system called iOS (which is also used on the iPad). Because it is written by Apple it is only used on Apple devices.
Another operating system is called Android (supplied by Google) but this can be used by many companies and you can have Android phones or Android tablets. For example the Samsung Galaxy runs Andriod.
A smartphone is one that can connect to the internet via 3G.
So an Andrioid Smartphone is one that use the Android operating system and used 3G to enable it to connect to the internet.