According to standards, add-in boards such as graphics cards can draw a maximum of 75 watts from a PCI-e slot on a motherboard. If a graphics board needs more than that to operate, the manufacturer of the graphics card adds an additional connector to the card so that it has more than one source from which to draw the power it needs, increasing the total amount of power the card can use.
A 6-pin PCI-e power connection on a graphics card adds another 75 watts of available power to the overall amount the card is able to draw, when operating in the computer.
If a card has a 6-pin PCI-e power connection, it is not optional, it's required for proper operation. You run the risk of random system malfunctions, possible damage to the system, and the computer may simply refuse to run at all, until the power requirements have been fulfilled.