After Joseph Smith translated the Book of Mormon he returned the plates to the Angel Moroni. Part of the reason was that a significant portion was "sealed" and not available to Joseph Smith for translating. At some point in time in the future the plates will be made available again and the "sealed" portion will be translated for us. 
 
Although we don't have access to the plates now - there were many men that were given the privilege of seeing the plates. They then wrote their "testimony" of this and their (3 and 8 witnesses) testimonies are included at the beginning of the Book of Mormon.  
Testimony of Three Witnesses 
Testimony of Eight Witnesses 
 
An interesting sidenote about the witnesses. Several of them became disaffected from the church, but in each instance every witness stayed true to his testimony even when they had no motivation to do so.