You already know that Flash is a vector based graphic program. Storing graphical information as mathematical formulae results in small file size. Additionally, Flash allows the reuse of a graphic (and other objects) once it is converted into a symbol.
So what are symbols
Symbols are the greatest strength of Flash. They allow reuse of graphics, buttons or movie clips without significantly increasing the file size.
Flash stores all symbols in the movies' Symbols Library. Once an object is converted to a symbol, it is automatically placed in the library.
Symbols can be dragged from the library and placed on the stage. This creates an Instance of the symbol. You can consider the Instance as a copy of the symbol. Further, Flash allows the properties of an Instance to be changed.
For example, in case of Graphic symbols, the size, rotation, color, tranparency and brightness of the symbol can be modified yeilding a completely different shape. However, since the graphic information is a copy, the file size does not increase much.
Consider the size difference between a Flash file and a 32 color GIF file.