Three men die in a car accident on Christmas Eve...
Three men die in a car accident on Christmas Eve. They all find themselves at the Pearly Gates waiting to enter heaven. On entering they must present something relating to or associated with Christmas. The first man searches his pocket and finds some mistletoe, so he is allowed in. The second man presents a cracker, so he is also allowed in. The third man pulls out a pair of stockings. Confused at this last gesture, St Peter asks, "How do these represent Christmas?" The man's answer: "They're Carol's."
This is a Christmas joke. The humor lies in the fact that stockings are normally associated with Christmas because people hang them up in order to try and get presents from Santa. This is not really a religious tradition, so apparently St. Peter didn't accept it as being related to Christmas and therefore asked him for more information. The quick-thinking man decided that a safer answer was to try and associate the socks with Christmas caroling (which could reasonably be considered religious in nature). The problem was that whatever lady named Carol that he stole the socks from is just named similar to the word carol, and therefore not really associated with carols at all.
So, it is funny because it is a pun, and it also has some absurd logic in it.