In object orientation, a class is a template for creating objects.
A class may declare which data elements can exist in a class and what their types must be, and it may also specify and even implement functions that apply to those data elements. Depending on the object system, a class may also specify how an instance is to be created and/or destroyed, how methods should be dispatched, what methods can exist in a class, etc. In dynamic languages like Tcl, what an object system does with a class is more flexible than, e.g., C++, which is more constrained by its static nature.
DKF: I like to think of a class as being the type of one or more objects, as well as a factory for those objects. Not all OO systems uses classes though (e.g. Self uses prototypical objects).
The string "class" is also used as an extension command name, at least within itcl.