The chicken feet are a part of the Chicken Set, a Holiday reward received from the 2007 Easter event event. They are worn in the footwear slot, and give no bonuses in combat.
If the "Flap" emote has been unlocked from the Stronghold of Security, when wearing all the pieces of the set, players can do an enhanced "Flap" emote where their avatar lifts off the ground slightly as if flying.
The items can be retrieved by from Diango in Draynor Village if lost or destroyed.
Their examine is a pun on the popular "Why did the chicken cross the road?" joke.