An assault rifle is a select-fire rifle that uses an intermediate cartridge and a detachable magazine.
Examples include the AK-47, M14 and M16. Select-fire is the capability to fire the weapon in either semi-automatic mode, or switch to burst fire or fully-automatic. Assault Rifles along with machine guns are highly regulated, and have not been available to the general public since the Gun Control Act of 1968. The term Assault Weapon is often confused with Assault Rifle, and falls under a completely different definition. An AR15 for example is not an assault rifle by definition. The following link has examples of different rifles that are often referred to as “Assault Rifles” even though they are not: CA Legal Tactical Rifles AR-15 rifles are commonly confused with the M16. AK pattern rifles are commonly confused with the AK47. Note that none of these have the select-fire feature and therefore are not classified as Assault Rifles: CA Legal AK style Rifles
For more detailed information and history you can go to: https://en.wikipedia.org/wiki/Assault_rifle