The Menagerie is a 6 player, matchmade activity with multiple rooms of "challenges" to fill up your meter to eventually face a final super boss with mechanics and carnage at each stage.
Staged around the Leviathan belly and other areas that you may have seen on the Leviathan Raids, you travel to each section against different mechanics and different types of bosses.
A new end boss will be introduced each week for the next 3 weeks and then a heroic version will become available which wont have matchmaking active due to the high power and co-ordination potentially required at that level.