It created the concept of freedom on the press which protected the press in reporting information they were told was true.
Prior to the Zenger Trial, the government could arrest any publisher who reported negative information about the government. It silenced the publishers and put them under the authority of the government instead of reporting to the people. Hamilton argued the concept of liberty in regard to the press. Just because information about the government was reported negatively didn't make it false and therefore the press should have the liberty to report the information.
The Zenger Trial is the foundation for freedom of press found in the First Amendment in the US Bill of Rights. The trial occurred in the 1730's but the ideas of liberty continued through the revolutionary period. The Patriots used this concept to report on the English government and Loyalists during the war. It would be an important right to include in the Constitution when the Founders agreed to basic rights afforded to the people.