How did privateering help/strengthen Elizabeth's navy?
The Royal Navy during Elizabeth's reign, although one of the most powerful navies in Europe, was fighting several European powers, including the Spanish and Dutch, whose navies were arguably the most powerful among European powers. During Elizabeth's reign, the design of ships of the line (the strongest of the combat ships) favored heavily armored, heavily gunned vessels that could take point-blank hits from enemy ships, survive, and return devastating fire. The goal of naval warfare was to capture, rather than sink, enemy vessels, which then could be sold and/or converted to the winner's use. Many English, Spanish and French warships began life in an enemy's navy.
The issuance of Letters of Marque to English privateers, which gave them the right to attack enemy ships, gave Elizabeth an significant addition to the Royal Navy that she didn't have to support economically. The privateers supplied ship and crew, and their entire goal was to attack and capture enemy vessels for profit. With that goal, privateers especially sought to have ships with a combination of just enough firepower to intimidate an enemy's vessel, usually a merchant vessel rather than a warship, and a speedy, maneuverable vessel. Privateering sparked a design change in English ships of all types, eventually including those of the Royal Navy, that emphasized maneuverability and speed.
Although English ships began to exhibit these improvements, other European navies' warships did not. When the most significant threat to England came with the Spanish Armada in July 1588, the combination of ship construction, speed and maneuverability of the English ships played a major role in the defeat of the Armada, which constituted one of the most serious threats to Elizabeth's reign.