Well in order to know about the Armature you have to know the different coils used for Motor and Generator.
Two types of Coils are used for Motors or Generators i.e Field Coil and Armature Coil.
But in today practices one can use Permanent Magnet in stead of Field Coil while designing or manufacturing a Electric Machine.
And you must know that Generator is for producing electricity from given mechanical power and Motor is to consume electricity in order to perform mechanical work. In short they are just opposite.
The Principle of working of Generator and Motor can be given by Fleming Rule (Right hand and Left Hand)
While in generator we need a magnet and if we rotate a coil or conductor in the magnetic filed a voltage will be induced (known as EMF or Electromotive Force) and that will be perpendicular to both the magnetic field and the direction of the coil was rotating.
Now in motor, if we place a coil in between a magnetic field and supply power to it, it will experience a torque and will start rotating.
In short Generator : provide magnetic filed and some rotation you get Electricty
in Motor : provide magnet and electricity and it will start rotating.
Now in order to create Magnetic field either Field Coil or Permanent Magnet is used.
And the main coil used for Motor (in which coil we provide electricity) and Generator (from where you get EMF) is called Armature Coil or simply Armature.
And about location, well one can fit it either on Rotor or Stator are depending on his/her design