Hudson's sword is his signature weapon. The elderly gargoyle took it from a Viking shortly before he was placed under the Magus' spell of stone sleep and has carried it ever since. ("Awakening: Part Two") The sword is notable as one of the few relics of the Middle Ages that the gargoyles use on a regular basis. When David Xanatos replaced the sleeping Hudson with a stone statue, he claimed that the sword was the hardest thing to replicate. ("The Price")
Hudson uses the sword as a way of compensating for his lack of speed.  The sword is incredibly sharp, and when Hudson puts his full strength behind a swing it is capable of slicing through metal and stone. In the modern day, Hudson soon learned that its reflective surfaces were excellent for deflecting laser fire. ("Long Way To Morning")
Although it is not clear what the sword is made of (Greg Weisman suggests that it is probably steel), the fact the Hudson could not use it to cut Oberon's hair indicates that it is not made of cold iron. ("The Gathering Part Two") 
When Hudson enters stone sleep with his sword, it sometimes turns to stone with him and other times does not. This is due to the Spell of Humility. The discrepancy is caused by Hudson's mindset at the time: when he subconsciously accepts the sword as a part of his ensemble, it turns to stone with him, but when he is aware of it as a tool then it will not. 
Although Hudson is shown using the sword for the first time in "Awakening" Part Two, he is occasionally depicted wearing it earlier than this. In particular, he is shown with his sword in the flashback at the beginning of "Reawakening", which takes place the night before Hudson acquires the sword.