SATA provides the 3.3V power to those hard drives that want to use it. If the hard drive uses 3.3V components on board (most do), there is no need to provide 5V->3.3V conversion circuitry on the hard drive circuit board, reducing the component count and cost.
However, hard drive manufacturers have been reluctant to rely on the presence of the 3.3V line, since when a molex->SATA power converter cable is used, the 3.3V power is not available. Thus, most hard drives use 5V/12V power exclusively, and create their own 3.3V power on board.
The ground lines are common to all power rails. Voltage is not added or subtracted like that, voltage is a measure of how positive or negative the line/pin is held at by the power supply. Ground lines are held at ground potential, i.e. 0 V. Current sourced from any power line is returned to the power supply through the ground lines. Multiple ground lines are used to a) handle the total maximum current flow (it is typically higher than what is considered maximum for the small individual contacts in the SATA connector), and b) multiple ground lines that lie in between the power lines decouple any noise from one power line to the next, providing noise rejection.