Answer: The key to which you refer is a small, “long-barrelled” silver key that Gandalf gives to Thorin at the meeting in Bilbo’s home, along with the map to the secret entrance to the Lonely Mountain. Thorin closely guards the key by hanging it on a chain around his neck throughout the entire quest.
When the group of dwarves arrives at the Western side of the Lonely Mountain, the location of the side-door according to the map, they find the door but cannot open it. The determined dwarves are “too eager to trouble about the runes or the moon-letters” and attempt to force the door open without success.
Step-by-step explanation: