This means you have a constitutional right to petition the government (including any government agency or official) to address concerns, grievances, or requests.
The government cannot pass laws restricting this right—though some may try. It is a fundamental aspect of free speech and civic engagement in America.
This provision is similar to the First Amendment of the U.S. Constitution, ensuring that New Yorkers can engage with their government without fear of retaliation or suppression, which has been essential in our 250 year old democratic experiment.
Basically, if you need legal expertise, you hire a lawyer. If you need help managing your finances, you turn to an accountant. And if you want to shape government decisions, you enlist a lobbyist.