The phrase "shall not be infringed" means something cannot be limited in an unreasonable manner. This phrase usually refers to rights and essentially means that, once a right is agreed on, it is an absolute right and cannot be limited later.
One well-known use of this phrase is in the Second Amendment. In part, it reads, "the right of the people to keep and bear Arms, shall not be infringed." A literal interpretation means that everyone has the right, and it cannot be limited for fear that it eventually becomes so limited as to be useless. The Supreme Court decides what counts as infringement or unreasonable limitations in a practical sense.