From A Wiki of Ice and Fire
Longclaw is a bastard sword or hand and a half sword, which means it is a good half a foot longer than a standard long sword, tapered to thrust as well as slash. With three fullers incised into the blade to reduce weight. There are ripples in the dark steel indicating it is of Valyrian steel.
The Mormont's had carried it for 500 years, and is given to Jon Snow by Ser Jeor Mormont because his son, Ser Jorah Mormont, had brought dishonor on the house. Ser Jorah had the grace to leave the sword behind before he fled, and Jeor had forgotten about it until he found it in the ashes of his bedchamber.
The fire that had killed the wight had also damaged the sword prior to being given to Jon Snow, melting silver on the pommel and burning the crossguard and grip, and Jeor Mormont had them replaced and repaired before giving it to Jon Snow. It once had a bear's head for the pommel, but this was replaced by a snarling wolf's head of pale stone with chips of garnet for the eyes to reflect Jon Snow's Stark heritage. The pommel is weighted with lead to give better balance.
Longclaw was passed down through House Mormont for about five hundred years. Jeor Mormont passed the sword down to Jorah Mormont when he stepped aside and joined the Night's Watch. When Jorah escaped justice to the Free Cities, he left Longclaw behind and Jeor retook possession of it.
In saving Jeor's life from a wight attack at Castle Black, Jon Snow set a fire that damaged Longclaw's hilt. Jeor had the hilt replaced with one capped by a wolf's head and gave the blade to Jon. Jon noted the appropriateness of a bastard wielding a bastard sword.