Special weapons are just that, special. Often they are represented in movies as the trick weapon or magical in some way. In real life they are represented by the master level weapon of a style. Hard to describe in any simple manner, special weapons are often the culmination of a given styles techniques. While weapons, on their own, can be classified as advanced or simple; special weapons are literally the next step. When you have trained all the style has to offer and have mastered all of the weapon skills of a given style, you will have a distinctive combination of skills. You now need one of two things; a weapon which builds even more skill or a weapon which efficiently uses all of the skills you have. Larger styles will often require that a student develop their own unique weapon as proof of weapon skill and understanding.
This is not merely making a sword longer or shorter. Nor is it simply putting a few more points on your throwing star. The water drawing swords, various Tai Dao, butterfly axes, yue yuan razors, and many other weapons you can find in your bud k catolog are a small glimps of the variations you can expect when looking for special weapon. There isn't even training for most of these weapons, you learn the whole style and you automatically know the weapon.