How did Andrew Johnson change the world?

Answer 1

It is not at all clear that he did. About the most important event of his presidency, in global terms, was the purchase of Alaska from Russia. Had this not happened, the Soviets might have had a foothold in North America during the Cold War. However, even this is debatable, as the purchase was mainly the work of Secretary of State Seward, and might well have still taken place under another president. For the rest, Johnson's term was mostly concerned with US dfomestic affairs like the readmision of Confederate states to the Union, which had little impact on the international scene