Henrietta Leavitt is a relatively unsung hero of astronomy. A graduate of Radcliffe College, she went to work--at first as a volunteer--at the Harvard College Observatory in 1893 examining photographic plates of images of the night sky.
In Leavitt's day, a star's distance from us was determined in part through a method known as parallax. No, a parallax is not two hammocks side-by-side or a semi-laxative. It's a process that is difficult to explain briefly in writing (for me), but it is summarized on Wikipedia, (see parallax), including this possibly helpful example from the entry:
A simple everyday example of parallax can be seen in the dashboard of motor vehicles that use an older-style "needle" speedometer gauge. When viewed from directly in front, the speed may show exactly 60; but when viewed from the passenger seat the needle may appear to show a slightly different speed, due to the angle of viewing.
Anyway, parallax as a method for measuring a star's distance only works with stars relatively close to us. Leavitt noted that stars with variable brightness (that is, they pulsate), known as Cephalids, exhibit a direct relationship between how bright they are and how long they're bright for. Her work used this finding to pushed out farther, beyond the parallax method, the maximum distance at which we can measure a star's proximity to us.
In the early 1900's, scientific opinion was divided as to whether or not all stars were contained within our galaxy. The famous astronomer Edwin Hubble would in the 1920's conclusively prove that some stars visible to us were outside of our galaxy--that is, really, really far away--which would more or less also confirm that our galaxy was just one of many, many galaxies.
He accomplished this in part through the benefit of Leavitt's preceeding work.
Before Hubble's discovery, astronomers were seeing other galaxies in their telescopes all of the time, but it wasn't a certainty what they were. They looked most or less like what one might call smudge-stars; they seemed to have shape and structure, but what the heck were they, really? Some scientists speculated that they were other galaxies, but, as I wrote above, there wasn't conclusive proof. Hubble provided that proof doing what scientists do: "building on" (including correcting, improving, refining, integrating, or simply using) the work of other scientists--some of them maybe long dead!) who built on the work of other scientists who built on the work of other scientists, and so on..... You get the idea. I hope. Hubble