Back in the day, astronomers didn't know if there were galaxies in the universe other than the Milky Way.
They could see blobs of stuff in the sky that looked like potential galaxies, but that could also be clouds of gas and dust on the edges of our own Milky Way. How to determine which they were? What was the true nature of these 'nebulae'?
On one side, enter Harlow Shapley. Shapley pointed out that it’s difficult to distinguish nearby, dim objects from distant, bright ones. But given how (relatively) small and bright these nebulae looked to us, if they were distant and comprised their own galaxies, they'd have to be INSANEly bright and far away to appear as they did to earthbound observers. Plus, astronomers had observed a nova in Andromeda that was brighter than the entire rest of the nebula combined-if Andromeda was a whole galaxy, what phenomenon had released so much energy so quickly?
Shapley’s opponent was Heber Curtis. Curtis believed that the nebulae were 'island universes' of their own, basing his opinion on the fact that the spectra of light from these blobs were indistinguishable from the spectrum of the Milky Way (whereas individual types of stars have their own distinct spectra). Not to mention, contemporary theorists were beginning to propose a spiral structure for the Milky Way, just like those of the mysterious nebulae.
In 1920, Curtis and Shapley had a Great Debate in Washington DC. Each scientist presented his arguments, but the debate ended in a draw.
But wait! Several years previously, an astronomer named Henrietta Leavitt (who, breaking gender barriers at Harvard, became one of the greatest researchers of her time) had discovered a relationship between period and brightness for Cepheid variable stars.
Variable stars are what they sound like: stars that vary in brightness over time, waxing and waning in the amount of light they emit. The period of a variable star is simply the length of time between one luminosity peak and the next.
Leavitt discovered that there was a fixed correlation between the inherent brightness of Cepheids, and their periods: brighter stars took longer to go through their full cycle of waning and waxing. Leavitt's groundbreaking research paved the way for the resolution of the Great Debate.
In 1924, (and stay with me, we’re almost done) a young man named Edwin Hubble used the 100-inch telescope at Mount Wilson, California to locate Cepheid stars within nebulae.
Because Leavitt had shown a relationship between Cepheids' periods and intrinsic brightness, and because Hubble could now measure the period of stars in nebulae directly, he could determine how luminous the Cepheids in the nebulae really were.
From there, it was a short step to settling the Great Debate. If we know how bright something is, and we know how bright it looks to us, we can tell how far away it is-resolving Shapley's dilemma of distinguishing close faint things from far bright ones.
As you (hopefully) know, our galaxy is not the only one in the universe. Hubble’s calculations demonstrated that the nebulae were so far away, they had to comprise their own separate galaxies.
Shapley wasn't all wrong: nebula-like 'globular clusters' do exist within the Milky Way, and the 'super'nova that had gone off in Andromeda WAS an unusual phenomenon.
But these facts weren't obvious at the time. Arriving at a less-wrong picture of the our universe took hard work and careful analysis. Today scientists estimate that the universe is billions of light-years across, but it's worth reflecting that a century ago, most people thought the Milky Way was pretty much it.