Simply put, a fixture is something that is permanently attached to real property (a house). Things such as ceiling fans, chandeliers, towel racks, built in shelves, carpet etc. Fixtures are always included in the sale of a home. The owner of a home cant unbolt everything connected to a home before you take possession.
Granted, a ceiling fan isnt really permanent. It could be uninstalled. But it IS an integral part of the home (unlike say, a piece of furniture) and is included in the sale of a home.
If you want to keep Grandmas chandelier, you need to either remove it before the home is listed, or have your agent be VERY SPECIFIC in listing the home and their conversations with buyers agents that the chandelier does not convey with the sale. (Itd be best to remove it and replace it with another light fixture to avoid any possible hassles. People HAVE lost Grandmas chandelier when they sold their home!)
What is and isnt a fixture confuses a lot of people. One of the biggest questions that comes up frequently is window coverings. Heres the scoop . Curtains are not considered fixtures. Curtain rods however, are. Mini-blinds are fixtures. Screens (and screen doors) are fixtures.
The best way to remember what a fixture is is this: If its attached (via screws, nails, glue, etc) to the walls, floors or ceilings, its a fixture. When in doubt, ask your agent. Hopefully you have a good one! If not, you know who to call!
Heres a very detailed explanation of fixtures from one of my favorite web resources, Wikipedia.org.