ive seen people take the top cover off that black box that connects to that black hose and the manifold, im kind of a car newb and i was wondering why they do this and what it does

 

whatever the reason is, it's retarded because it exposes the filter to hot underhood air which reduces performance.

 

Also, the stock filter isn't designed to run "open".

 

Actually, the stock design is to pull air next to the air box (still inside engine bay, still hot air). The reason people would open the air box is that they THINK they can get more hp by less air restriction. (Same idea as any old style intake, hot air intake).

It is a really bad idea. you can increase at most 1 peak hp, but you will lose a lot of hp in lower rpm. And it is especially bad when the car is at low speed.