Toyota 4 Runner 1995 Identify Hose

I had work done on my Toyota 4runner 1995 and they messed it up. I brought it in to change manifold gaskets and now I have all sorts of issue. I even have an error 71. When I drive, i feel some rattle, like something shaking in the engine. but after 25mph the car drives fine, but when I come to a stop I feel it again a bit. I noticed on the photos attached I found online, that on the red circle area, theirs a hose with two sides. What is that hose called? also what would occur if they didn't put that house and just cover the whole in red?