By "large dresses" I'm assuming you mean long skirts, more layers of undergarments, a higher level of ornamentation, etc.? Please correct me if I'm wrong! But I'll answer on that assumption for now.

It's difficult to pinpoint the period of the simplification of women's dress as there's a certain amount of back-and-forth rather than a straightforward progression (like all trends in history). For much of the 19th century, as one aspect of dress became more streamlined, another ballooned out. In 1836-1837, the previous full sleeves were pleated down tightly along the upper arm; at the same time, a lot of fullness was being added to skirts. High fashion in the mid-1860s favored a look with fairly little trim, but the early 1870s saw more intricate effects becoming popular. With the demise of the bustle (and the fashion of overskirts) in 1888-1889 came the rise of the large sleeve ca. 1892.

The strong transition toward a more pared-down fashion really starts as the sleeves shrank back again in 1897 and 1898, because nothing really replaced them as an exaggerated aspect of fashion the same way that waning features had previously been replaced by waxing features. After being tight for a few years, the sleeves did take on some more shaping - a curve or puff near the wrist 1902-1903, gaining some fullness at the shoulder in addition to that 1904-1905, then keeping that but losing the volume in the lower arm 1906-1908, narrow sleeves coming back in 1909 - but none of these were as big as the big sleeves of the mid-1890s. Similarly, the skirt saw shifts in cut - going from a tulip-shaped flare in the early years of the decade to a more narrow, straight profile at the end of it - but apart from a stylish form of dress in the 1920s which made use of wire-stiffened panniers to hold out the skirt, the idea of an actual structure worn under the petticoats to create an artificial shape for the skirt was gone as well. Dresses of the 1900s, 1910s, and even early 1920s could still be more complex and fitted than dresses today, but these ensembles are certainly more simple than those from the decades before.

Now, as to "why" ... well, one part of the answer is that fashion is not constant. It doesn't really move on a trajectory in a really long-term sense: even during those centuries of "large dresses", there were swings into narrower silhouettes and simpler cuts. It is possible that in two or three hundred years, we will be looked at as an anomaly, a short interregnum between "large dress" periods. But in the specific case of the early 20th century shift, I would say that a large part of it was the general desire for convenience and functionality that you can see throughout material culture at the time. Art and design (from furniture to cars to kitchenware) moved into pared-down Neoclassical and then Art Deco styles. Time/motion study was used to get people working in the home or in factories to use the most efficient movements and floor plans. Using excessive amounts of fabric or potentially hampering the body was philosophically unwelcome, so fashion responded to that mindset and complied. There was also a certain feeling that fashion of the past had been extreme and oppressive, not the kind of thing that modern and enlightened people would have any truck with, which unfortunately still affects the lay perception of historical fashion.

(Answer to your bonus question tomorrow.)