Muktzeh is a Hebrew word that means "separated", or "set aside". The generally accepted view regarding these items is that they may be touched, though not moved, during Shabbat or Yom Tov. Some extend this prohibition to the actual handling of these items. Halakha defines various categories of objects or substances which are "set aside" on the Jewish Sabbath, as well as various permissible instances of moving these various muktzeh items. For example, one may not handle money, rocks, twigs, etc. on Shabbat, as these items are muktzeh. The consensus among the halakhic authorities is that muktzeh is an issur d'rabbanan, rather than a d'oreisa. The laws of muktzeh can be divided into two distinct subjects:
"Muktzeh", i.e. the conditions needed for something to become muktzeh, and the properties of the various categories thereof;
"Tiltul", i.e. if an item is indeed determined to be muktzeh, it must be determined when and how it may be moved.
General concept
Muktzeh is essentially a restriction on objects that were not 'prepared' before the Sabbath. The absence of preparedness in this sense means that when Shabbat began, the vast majority of people would not have expected to use this particular item or substance on Shabbat.
Categories
There are six main categories of muktzeh, each one with different halakhic ramifications:
Mechamat Chisaron Kis: delicate objects which one is extremely careful when handling; e.g. a musical instrument or camera.
Basis: an object supporting a muktzeh item, which takes the same status as the muktzeh item; e.g. the trayholding the Shabbat candles.
Mechamat Gufo: objects that are not utensils and have no ordinary Shabbat function; e.g.raw foods.
Mechamat Isura: objects whose use was totally prohibited because of Shabbat violations when Shabbat began remain muktzeh all Shabbat; e.g. Shabbat candles.
Kli Shemlachto L'isur: objects designed primarily to perform forbidden work; e.g. a hammer.
Mechamat Mitzvah: objects used only to perform a non-Shabbat mitzvah; e.g. a lulav.
Chai Nosei Et Atzmo is a Hebrew term meaning, "a living thing carries itself". It is a concept in the field of muktzeh, specifically an exception to the general rule that one cannot carry an object from a private domain into the public domain on the Sabbath. There is a debate between the Sages and Rabbi Natan over whether this rule applies only to humans, or to animals as well.
