This painting, while an extremely important example of Leonardo's and High Renaissance art, did not have an impact on "the world" in general. Paintings generally don't. They may reflect their eras, their artists, certain social and cultural issues, and they may be influential as far as other, later artists are concerned, but they don't affect the world.
"The Last Supper" has been much copied and parodied, so in that sense, it's one of those famous works (like the Mona Lisa and Michelangelo's Creation of Adam in the Sistine Chapel) that has moved into the general public consciousness to the extent that even people who don't know much about art recognize it. But it has had no general or substantive public, political, religious, or social impact on the world.
If you'd like to understand the painting about as thoroughly as it can be understood, I recommend Leo Steinberg's book "Leonardo's Incessant Last Supper," published in 2001. Dr. Steinberg is one of the major experts on the work.
