A ship's rig is the entire structure used to support and maneuver sails. This includes the masts and spars, but also many miles of rope in the form of standing rigging and running rigging. Standing rigging lines support and stabilize the masts while running rigging is used to move the parts.
Active working ships must maintain their rigs to keep them structurally safe and in good working order. Normally this involves "downrigging" about once every 1-5 years to inspect and replace worn parts.
Museum ships like Constellation should ideally downrig every 20 years or so for the same reasons. This project will overhaul and replace any worn parts of the rig as well as reinstall the rig with the lines and supports tightened and secured.