That's the charcoal canister, and it is not in the airflow path; it is in the air cleaner cover. The intake is on the passenger side of the cleaner body, the filter is on the driver side, charcoal pack above.
I believe the purpose of the charcoal is to pick up stray fuel vapors that may escape the intake manifold/throttle body. Part of the atkinson/miller cycle has fueled air in the cylinder to leak back out the intake valve during the early part of the compression stroke.
I believe this is also why you get the shudder when the engine shuts down during a trip especially when it is still cold; the engine is still given spark but no fuel to burn off any remaining vapor in the intake manifold.
You'll find both rabid fans of it and also those with high contempt of it. My understanding is that it's reusable and supposedly takes more junk out of the air intake, but there's also concerns that the oil isn't good for the engine and it also lets too much air (and therefore particles) through it.