A cloaking device is a form of stealth technology that uses selective bending of light to render a starship or other object completely invisible to the electromagnetic spectrum and most sensors. It has been encountered in varying forms over the centuries.
Why does the USS Wolff have a cloaking device?
Since 2311, the Treaty of Algeron between the United Federation of Planets and the Romulan Star Empire had forbidden the Federation from pursuing any cloaking technology. However, covertly, Starfleet did indeed develop not only a cloaking device, but a phase-cloak. This enabled any ship so equipped to pass through any ‘normal’ matter, such as a planet or asteroid.
Following first contact with the Dominion, the Romulan Star Empire entered into a joint intelligence gathering operation with Starfleet. The Romulan government loaned a cloaking device to Starfleet to be installed aboard the starship USS Defiant. In return, the Romulans were allowed full access to any intelligence gathered from the Gamma Quadrant by the Defiant. This began a period of decreased hostilities with the Romulans, culminating in a full-fledged alliance, which helped bring an end to the Dominion War.
With the Dominion War over, the RSE finally agreed to an amendment to the Treaty of Algeron permitting the UFP to deploy cloaking devices on all Federation starships, providing no ship utilizes a phase-cloak.