What does He has obstructed the Administration of Justice by refusing his Assent to laws for establishing judiciary powers mean?

It means that King George was making it difficult (or impossible ) to process court cases and administer justice by refusing to agree to local laws establishing courts.

This charge pertains to a situation in North Carolina that originated from an act of the English government disallowing a law passed by the North Carolina legislature for establishing courts of justice and regulating their proceedings. The English objected to this law on the grounds that the establishment of courts of justice was an action reserved to the sovereign power, which belonged solely to the King. As a result, North Carolina was compelled to do without courts of law for a long time. Similar situations existed in South Carolina and Pennsylvania. These were all violations of the principle that just government derives from the consent of the governed, and that government exists to secure rights. Without a judiciary to punish criminals and to enable injured individuals to sue the injurer for redress, life, liberty, and property will be insecure.