Thingamajigger... what is this?

I got a cold air intake a couple of days ago and was wondering what these lines on the back of the air filter box do so I know what to with them after the box comes out. Just wondering

one is the air intake sensor .... hook it up to the hole in the cai

thats what I thought the black cillynder was for but what about that second one that goes to the Intake Manifold?

it goes to the intake manifold or the valve cover ?

manifold on the right side after where the TB hooks up