Shaolin Quan (少林拳) (in Cantonese Siu Lum Kuen) is the term typically used to describe the martial styles that originate from the famous Buddhist Shaolin Temple in Henan, founded in 495 C.E. by Ba Tuo.
Ba Tuo had a keen interest in Wushu and as such Shaolin Temple became a tolerant haven for the practice of martial arts. It was some 60 years after its founding that the Temple received a visitor largely regarded as the father of Shaolin Martial Arts, an Indian Monk named Tamo.
Tamo, or as he is also known, Bohdidharma, came to Shaolin to introduce a new form of Buddhism we know as Chan Buddhism (Zen in Japan). Upon his arrival at the temple he found the monks in poor health and unable to endure the long sessions of meditation he introduced. Tamo retreated to a nearby cave and meditated for 9 years. (There are multiple versions of the Tamo story, this is merely one). During this time Tamo created two exercise regimens: The "Muscle Tendon Change" and "Marrow Purification" forms. One for strengthening the physical self the other for strengthening the spiritual self.
The monks of Shaolin combined the movements of Tamo's forms with those of the existing martial arts of the area. This was the birth of what is known as "Shaolin Quan". Over the following centuries it evolved into what is highly regarded as one of the highest forms of martial arts.
Shaolin Wushu began to take the shape we see today during the Ming Dynasty (1638 - 1644). During this time Shaolin blossomed as never before. Typically within the Shaolin system, there are ten empty hand "sets" and various weapons. Weapon training will vary from school to school. The Shaolin practitioners are unparalleled in the use of the staff and spear.
The two main schools of Shaolin Quan are the Temple style and the Northern style (Bak Siu Lum style). Both of these consist of ten hand sets and although similar in technique the sets are completely different.
There are of course many styles that trace their origins to Shaolin and or are influenced by it, yet they cannot be called "pure" Shaolin Quan.