As an autograph dealer, your primary job is to ensure the authenticity of the material that you sell.  This means that when you sell an autograph, you have rendered the sole opinion on its authenticity.  This is where the market for the third party authentication was created.  Basically, it is a second opinion given by a company that specializes in such things.  They provide an additional set of eyes that agree with the opinion of the original seller.
Third party authentication is also useful if, as a collector, you have an autograph whose authenticity you want verified. Maybe the autograph came from a friend or was purchased online through a dubious source.  Or maybe you obtained the autograph yourself through an in person meeting or through an autograph convention.  In these cases, you might want documentation that says the autograph is authentic.  For this, you would need third party authentication.
With third party authentication, remember that the employees who work for these companies must have the same kind of experience that a reputable dealer might have.  And at the end of the day, you have no idea who actually looked at your autograph.  After many decades in the industry, we have numerous personal friends that have worked for some of the top third party authentication companies.  Some of them really know what they are doing, and some of them do not.  It is a fact that some authenticators use our website to find exemplars on autographs with which they are unfamiliar.  Third party authentication is generally a good concept, just be aware that these companies are not infallible.