Cloning is a revolutionary alternative to the ole "grind through an alt again" method of trying new classes. Cloning basically makes a "copy" of your current character, with no assigned skill points and gear. Your attribute points however, do not get reset. Some people do not set their attribute points until a much later level because of this.
Usually cloning is used just before you have to select a new class from the class tree. This allows you to try the other options without having to re-level all the levels on a new character. You can then experiment with the different options and see which class fits you better.
Cloning requires cloning credits. You can obtain these at key levels where you have to make a class change choice. You can also obtain cloning credits by completing the "Targets of Opportunity" missions from each zone.
A side note: cloning is not recommended at level 5.