That was a hose that a shop here had messed up on my car when they were installing the new turbo and intake. It takes the crank case fumes and puts then back into the systemm to be burnt up or put out thru the exhaust. On mine it was a y hose that came from 2 points in the engine and back into one point in the intake. It was a rubber and hard plastic piece that was like $150 fromm the dealer. The shop tried to just push the broken plastic part back into the lower crank case and it caused a check engine light to come on cuz of emissions control. But the original piece sure didnt look like that thing one yours now.

 

... it's pretty ghetto!