It means that the People, when wronged, are allowed to petition the government for a repair to the offending law, action, business, etc.
Definitions (not relevant to the answer but may help with understanding)
Petition: A formal written request. It's almost always signed by a lot of people, all of whom support & advocate for the written cause.
Redress: To fix an issue, to correct it
Grievance: A wrong, be it real or not, that provides reason for complaint.