A Wardwoven chest (the one with the icon above) is an extra reward for keeping at least one stack of Zoltun's Warding until completion of the Vault. Extra Loot!
A Sorcerer stands before a Statue of Zoltun Kulle offering a Pearl of Warding and in return, he will be given ten stacks of Zoltun's Warding. Keep one stack intact and you'll get a Wardwoven Chest at the end of the dungeon, keep four stacks and you'll get a Rare Wardwoven Chest too.
The Loom is an ancient technology designed by Zoltun Kulle and Ayuzhan to shape the elements and build tools to serve humanity. This is in the same room as Malphas who you battle at the end of the Season 3 Questline.
Traps in The Vaults are activated in Season 3: Season of Construct. The traps can not be deactivated so you must make your way across tentatively to preserve your stacks of Zoltun's Warding. Each trap you get damaged by removes one stack.