One of the amazing things about astronomy is that it mostly involves standing at one distinct point in the entire universe—Earth—and measuring properties of the light that happens to reach us here. That also means that our understanding of space deeply depends on the quality of the technology we've developed to look outwards, into the universe. In his dissertation on "Photographic investigations of faint nebulae," Edwin Hubble began: "The study of nebulae is essentially a photographic problem for cameras of wide angle and reflectors of large focal ratio."
When Hubble started his professional work in astronomy, in 1919, a new piece of technology—the 100-inch Hooker telescope—had just been put to work, at the Mount Wilson Observatory, where Hubble, too, was beginning to work. He pointed that telescope at nebulae and started taking pictures of them.
No one was quite sure what nebulae were, exactly. Their "essential features," Hubble wrote in his dissertation, were that "they are situated outside our solar system, that they present sensible surfaces, and that they should be unresolved into separate stars." But when he started looking at nebulae through the new, more powerful telescope, Hubble found that he could see stars—individual stars—in some of them, including Andromeda.
The first known recording of Andromeda was made in the 10th century, by the astronomer Al-Sufi. Europeans have been studying it since the 17th century. Now, Hubble saw that it included individual stars, and that some of them were changing in brightness.
This was the key. A little more than a decade before, the astronomer Henrietta Leavitt had shown that, when a star's brightness changes over a short period of time, that change could be used to measure its distance from Earth. When Hubble measured the distance of the variable stars he found in Andromeda, he found that they were nearly a million light-years away—way beyond the boundary of the Milky Way.
Before Hubble made these measurements, astronomers were arguing over whether the Milky Way was all there was. After Hubble's measurements—just 90 years ago—it was clear that wasn't true. There were other galaxies far, far away. And once it was clear there were other galaxies, astronomers could start looking at their relationships to ours. Just a few years later, Hubble showed that these galaxies were moving away from ours, some at a faster rate than others. A universe not only existed outside our galaxy, but it was expanding.