Jon Snow is the supposed bastard son of Lord Eddard Stark of Winterfell. In actuality, he is Aegon Targaryen, son of Rhaegar Targaryen and Lyanna Stark. He was a steward in the Night's Watch. Now serving on the Wall, Jon has found a place of acceptance where the circumstances of his birth are of little importance. He has a pet direwolf named Ghost, and wields the bastard sword, Longclaw, which was a gift from Lord Commander Jeor Mormont, who took Jon as his personal steward and came to see him as a surrogate son. After Jeor's death Jon was elected Lord Commander but due to his good attitude towards the wildlings he was murdered by his brothers of the Night Watch. In the show he was resurrected by Melisandre, who believes he is the reincarnation of Azor Ahai.
Powers and Stats
Name: Jon Snow, Aegon Targaryen (named by Lyanna Stark)
Origin: A Song of Ice and Fire
Classification: Human, King in the North, former Lord Commander of the Night's Watch
Attack Potency: Wall level (Somewhat comparable to White Walkers, met strikes from a White Walker on 2 occasions)
Speed: At least Athletic Human (Able to dodge strikes from a White Walker, who are faster than a normal human)
Lifting Strength: At least Athletic Human
Striking Strength: Wall Class (Can cut wights in half with little difficulty)
Durability: Wall level (Survived a hit from a White Walker)
Range: Extended melee range
Standard Equipment: Longclaw, his bastard sword
Intelligence: Trained from a young age in traditional Westerosi martial skills (Swordsmanship, archery, riding and etc.) and received an education on par with most Westerosi nobles.
Weaknesses: Despite being skilled and well trained, he is young and somewhat inexperienced as a fighter. He is a poor battlefield commander who was nearly defeated by Ramsay Bolton until he was saved by the knights of The Vale.
Note: This covers the show version of Jon Snow.