An assault rifle is a select fire shoulder arm chambered for an intermediate power rifle cartridge capable of being fed from a detachable magazine.
Typically an assault rifle is the standard issue weapon used by military forces. The United States uses the M16A2/3/4 as its standard rifle, though there has been a movement towards the M4A1 carbine (also an assault rifle).
The "MA5B Assault Rifle" from the popular Xbox game "Halo: Combat Evolved" is not an assault rifle because it is not select fire and it is chambered for a full power rifle cartridge (7.62mm x 51 NATO). It would be more correct to say that it is a magazine fed machine gun.
Some examples of real assault rifles include: the M16 series and the AK/AKM series.