Leica lenses (and the complimenting camera body) simply take better, sharper photos.
I know this does not sound right, but one can pick out Leica shots from non Leica shots - sort of the difference between a Brownie snapshot and an Ansel Adams print.
An optical physicist explained it to me this way: "With modern computers and lens design software, most any competent lens designer can design a good lens. The problem comes in the execution of the design. Lens construction require CRAFTSMANSHIP. The tolerances which must be met to fabricate a truly excellent lens are finer than those available to mass production. Thus, the super lens requires far more time consuming skill, steps, and finesse than a volume produced product - hence the higher cost."
But there is still more to a Leica lens. The designers also go the extra mile in the design stage. The computer can make the computations, but it cannot create the best design by itself. The lens designer has to "play" with the design to optimize it.
An example: Joseph Schneider (a very competent German lens maker) designed (and built) a special "shift" wide angle lens for Leica. The Leica lens designer took a look at Schneider's design and came up with several small improvements, which Schneider subsequently incorporated into the lens.
A factor which is critical to the perceived "sharpness" of a lens is its contrast. Leica lens designers tend to be fanatical at delivering high contrast, even in the corners, and at wide open aperture. A key part of this is controlling dispersion of the light as it passes thru the lens. In layman terms, one can readily understand that if some of the light gets dispersed from, say the highlights, then the highlights will not be as light and bright as they should be. Since the dispersed light has to go somewhere, it will lighten the shadows. So there goes your contrast ! In addition, at larger (smaller number) apertures, more light is coming thru the lens, thus the greater impact of the dispersion on the contrast of the delivered image.