South Pass was very important to the westward expansion of the United States since it allowed for an easier passage than the Northern Route taken by Lewis and Clark in 1805-6. This is also where it got its name from, being the 'southern' passing, directly across the Continental Divide at a gradual slope as opposed to the more treacherous northern one.
Timing your journey on the Oregon Trail was important regardless of the route you took. Since the journey was so long and covered so much uninhabited territory (or at least uninhabited by settlers/westerners), leaving too early or too late could spell disaster and death for a wagon train. If you left too early, there wouldn't be enough grass to sustain your oxen and livestock as you crossed the plains. If you left too late, you risked running into snow storms in the mountains before you arrived at your destination. additionally, you had to avoid arriving too late in the season to be able to build a home once you settle since raw materials were harder to come by in winter. Therefore, settlers needed to get to South Pass with enough time to replenish their supplies and then leave South Pass with enough time to beat the snow.
The other issue particular to South Pass was the Green River. Depending on where they crossed, wagons had to either ford the river or pay a ferry to take them across. This crossing was very dangerous and many drowned attempting it. If the conditions were poor due to high water levels, the crossing was more dangerous and more expensive. During peak travel months (May, June, July) there was often so many trying to cross that there was a wait of several days. This not only caused an inconvenience because of the poor, overcrowded conditions in the camps on the banks of the river, but also because it could cause costly delays to the whole journey.
The three sources below are useful when studying South Pass.