What is this black plastic thing under the hood?

Looks like you are talking about the Snorkel.

The outside air flows through it to the engine filter box -- unless mice have made a nest in it. I take off the connection at the engine filter and put the shop vac on it every once in awhile to clean it out -- per Patrick Wong's advice.

Hobbit, one of the earliest experts on the Prius actually thought it a worthless piece of junk that was in the way, apparently, and removed the snorkel on his Prius altogether.

The driver of this Oregon Prius apparently thought the car needed a bigger snorkel.






Here it is out of the car.

 

Part of the air intake system as cyberpriusII already posted. It’s normal for that end peace that you did circle (that’s not in the cyberpriusII picture) to be lose. It just pushes in to the part on the picture and is attached with one clip from the top. You need to remove that peace to change headlight.