The mechanical hound is this mechanism that is used to hunt down and kill people who have in some way violated the laws of the society. It is made of metal and is called a hound even though it has eight legs.
The main place where we see the hound is in the pursuit of Guy Montag. After Montag kills Captain Beatty, he is an outlaw. The hound comes to kill him (by poison) right away, but he manages to evade it. He then makes his way to Faber's house where he drinks something that changes his odor (so the hound can't find him). The hound eventually is programmed to kill someone else who is said to be Montag but is, of course, not him.
So, its purpose in the society is to kill people who break the laws. I think its purpose in the book is to show how (by serving as a symbol) faceless and mechanical the system is in this society.
In the novel Fahrenheit 451, the Mechanical Hound is a robotic dog with eight legs used to track down and kill fugitives in Bradbury's dystopian society. The Mechanical Hound lives in a kennel inside the fire station and eventually chases Montag as a fugitive towards the end of novel. It has an amazing ability to track virtually any scent and has a four-inch steel needle that projects from its nose to inject procaine into its victims. It is a creation of perverted science used by the authoritarian regime to control its populace. Towards the beginning of the novel, Captain Beatty sends the Mechanical Hound to sniff around Montag as a warning. After Montag becomes a fugitive of the state, the Mechanical Hound hunts him and stabs Montag with its needle. Fortunately, Montag is able to incinerate the Mechanical Hound and escape the authorities.