This is a phrase used in America during the celebration of Halloween. At Halloween, children dress up in costumes and go from door to door and knock. When the door is opened, the children will yell "Trick or treat!". The person will then put a little candy into each bag that the child carries. The term "Trick or treat" refers to the old custom that if no candy or treat was given, a trick would be played on the person. When I was young, the trick usually was to put soap on the windows. Actually, these days, the parents accompany the children from door to door and would not allow them to play any such tricks. I hope. The kids still say "Trick or treat", though just because that's what they've always said. Halloween is also called All Hallow's Eve. It is on October 31, which is All Saints day in the Catholic church. As far as I know, the custom of dressing in costume comes from the fact that people on the evening before All Saints day would dress up in scary costumes to frighten away evil spirits. Someone can correct me on this if I am wrong.

it is short for 'give me a trick or a treat'

This American custom has been in Australia for many years as well, although I am not sure how popular it is in other countries.

This is used at Halloween, when children dress up as ghosts and witches and knock on strangers doors asking for sweets/candy. They say "trick and treat" to mean that the person opening the door can either give them the candy (treat) or they have a trick played on them (something nasty - normally they will have eggs thrown at their house). I was never allowed to go "Trick or Treating" because we saw it as threatening people that we didn't know, especially old people who sometimes get very scared if they are alone, late at night on halloween. It is also dangerous to knock on the doors of strangers! However, it is a very old tradition that is very much alive today :)