The genius of the camera was not the interchangeable lenses (that was introduced in 1930 for the 39mm screw mount, and in 1954 with the Leica M3 and the M mount), and not the rangefinder focus method (Leica II in 1932). The genius of the ur Leica was the use of ordinary 35mm motion picture strip film in a compact camera.
Barnack placed the film horizontally, since he thought that the 18x24mm cinema frame was too small for a quality photo. The resulting horizontal 24x36mm frame has since become what we call "Full Frame" today, and people pay a large premium for cameras and lenses that accommodate this imaging size. Ironically, the film size was seen as a miniature format at the time.
Putting the film horizontally also yields the rectangular camera shape that we are used to even today. With the small size, the camera was intended to be used during hiking, for landscape photos.
The ur Leica was revolutionary, since it allowed people to easily carry around a quality camera, not needing to set up a big field camera on a tripod and pose the people in the frame. This allowed people to take quick snapshots, a completely new style of photography.
The actual product was not launched until 1925, and did contribute to changing photography.
So what is the Leica of today? What is the camera that people always bring along, and makes it easy to take snapshots? The answer is obvious: The camera phone.
The smart phone now allows people to take better pictures than before, and has been a revolution for photography, even if it is often dismissed by enthusiasts.
Today, Leica innovation is more about creating status symbols than bringing photography to the masses. We see this in their newest product, the Leica T mirrorless system. As a photography tool, it brings nothing new to the table. It is a very nicely finished camera, though, at a very high price.
This is often what happens with strong brand names. In the end, it is more about selling the brand name, and less about the products.
In Micro Four Thirds, we now know the term "Leica" as a brand name for some of the premium lenses from Panasonic. For example, the Leica 25mm f/1.4 (my review), which I think is a fantastic lens. However, these lenses are hardly related to Leica, beyond the branding. Some evidence even suggests that Sigma designed the Lumix/Leica 25mm f/1.4.
So today, the Panasonic/Leica partnership allows Panasonic to use the Leica brand name for their premium lenses, so that the market trusts them as quality product, and it gives Leica more volume and production capacity.