it means that the aircraft is pressurised to the equivalent air pressure you would expereince if you were 6000 feet up a mountain.
The aircraft is designed with a "maximum pressure differential" in mind that means roughly that when you are flying at 40,000 feet your "cabin altitude" is maybe 10,000 feet.
The 787 is designed to fly direct city to city pairs and avoid the congestion horrors of flying to Heathrow, Chicago, Atlanta, Sydney Houston Narita etc.
It is thus the direct competition to the hub and spoke model that the A380 caters to.