What is positive air pressure?

Computer chassis are typically equipped with many case fans, some are designed for exhaust and others for intake.  When intake fans’ combined airflow is greater than exhaust, a positive pressure is created inside the chassis.  Conversely, when the airflow is greater for exhaust than it is for intake, a negative pressure is created.
How does positive and negative pressure affect airflow in a chassis?
The major difference between positive and negative pressure is the way vents and various gaps are affected.

This photo shows an example of a modern high performance chassis with extra vents not occupied by case fans.  These vents can become either exhaust or intake depending on whether the chassis has positive or negative air pressure respectively.

*Dedicated vents aren’t the only places on a chassis that can act as pathways for airflow, gaps on the outside the chassis such as the one shown in this photo can also be affected.

The benefit of having positive air pressure:

Benefit 1: Dust reduction
  Newer case models now sometimes include fan filters in an attempt to reduce dust build up inside the chassis.  If the chassis has positive pressure, only intake fans require fan filters to effectively reduce dust build up.
The diagrams show that chassis with positive air pressure can prevent dust from penetrating into the chassis by use of filters on intake fans and forcing air out of the chassis through unfiltered vents and gaps. On the other hand, a chassis with negative air pressure draws in air from unfiltered vents and gaps that even with fan filters placed on key intake fans, dust can penetrate into the chassis easily.
The idea to use positive air pressure in designing dust-proof chassis comes from the concept of a cleanroom. The cleanrooms are used often in Hi-tech, medical, and food processing industries.  All cleanrooms, regardless of their levels and sizes, are built to maintain a positive pressure environment to prevent dust from entering the room.

Benefit 2: Maximize graphics card cooler’s efficiency
Left: Partially sealed graphics card cooler      Right:Fully sealed graphics card cooler

   Currently, all original graphics card coolers (non-custom) are designed to exhaust air toward the rear to prevent heated air from being recycled back into the chassis:

Partially sealed graphics card cooler:
Diagram A:Heated air are blown partially out of the chassis with the rest remaining inside the chassis

Diagram A-1: In a negative pressure chassis, heated air that is suppose to be blown out will re-enter the chassis through openings nearby and raising the chassis temperature.

Diagram A-2: In a positive pressure chassis, all heated air from the graphics card will exit the chassis, keeping overall temperature low.
Fully sealed graphics card cooler:
Diagram B: Fully sealed graphics card does not exhaust heated air into the chassis, but the fan in the cooler is affected by the pressure inside the chassis.

Diagram B-1: In a negative pressure chassis, the air from outside will try to enter the chassis through all openings, including the graphics card exhaust opening.  As a result, the fan in the graphics card cooler need to work harder to push the air out, becoming less efficient and likely to be more noisy.

Diagram B-2: In a positive pressure chassis, air will try to escape out of the chassis through all openings and exhaust fans. As a result, the fan in the graphics card cooler, which is designed to exhaust air out of the chassis, will work more efficiently with increased airflow and less noise.

Both Sugo SG03 released in 2007 and the Fortress FT01 released in 2008 are examples of chassis with positive air pressure design.  They have optimized support for high-end graphics cards and filters to prevent dust built ups for longer service life.