The simplest explanation is to think of Phases like gears -- however not all MOBO's utilize the Phases in the same precise way. Like gears in the case of LGA 1155 (12) seems to be the magic number in offering a smoother transition as the power requirement goes up from load on the SB CPU. The smoother transitions yield improved stability in voltage which tends to yield a lower vCore. There are MOBO's like the Gigabyte UD7 series which offer 24 Phases but the vCore advantage yields diminishing returns.
In contrast (16) Phases was the magic number for most LGA 1366 MOBOs.
So the question is 'How do I know this?', I looked CPU-z Validated data and studies comparing MOBO's to vCore e.g. ->
http://www.overclock.net/t/916189/official-intel-p67-z68-motherboard-comparison-list-oc-results
I am still trying to figure-out the SB-E/LGA 2011 so called magic Phase number.