This is quite a subjective question, so there are not really right or wrong answers but I will give you my input. In terms of hard physics there is the somewhat old discovery of spectroscopy. This was found by people doing classical physics but requires a quantum description to know why it happens. The underlying physics are beyond the scope of the question, so I will tell you what it is and why it matters so much.
When a gas is heated to a high temperature it gives off light. We are familiar with this phenomenon, we see this in fluorescent light bulbs, neon lights, and street lights to name a few places. But the impact of this discovery is not due to its illuminating properties. The amazing part is that every element has its own frequency signature. What does this look like?
If you take an illuminated gas tube (like a neon light or a sodium-vapor flood light) and pass the light through a prism, you will not get a rainbow. You will get a few lines of specific colors that would be located on the illuminated surface where the whole rainbow would normally be found. Most of it will be dark. What happened to the other colors? Atoms in a gas only have the ability to "shine" at certain frequencies. That is, can only emit certain colors of light. Since every element is unique in its ability to emit light, you can tell what atom is being made to glow based on the emitted spectrum.
"So what?" you might ask. Why does this impact us here on earth? We already know the gasses we put in our street lights! Well, it is in fact a big deal. Why?
Not only do atoms emit certain frequencies, these same frequencies of light are absorbed by atoms. (They resonate at these frequencies, so the physics behind why they create these frequencies is similar to why they "soak" them up and re-emit them.)
What does that mean to us? Here's the point of all of this: Stars have atmospheres made of gasses. These gasses absorb and re-emit light at random angles. Other frequencies of light pass right through the atmospheres like they pass through glass. The atmospheres are transparent to these other frequencies. So when we look through telescopes at distant stars we see almost white light. Why almost? Because the star's atmospheres (made of the same atoms as the stars) absorb and re-emit the light leaving the stars at random angles. Therefore the starlight that we see is missing certain frequencies because they were absorbed at the star surface and bounced off into space at random angles by the atoms in the atmosphere of the star. In other words, we know what elements make up stuff in the universe without actually going there and measuring it. We can take a "chemical sample" of anything that light passes through, too, because it scatters certain frequencies, keeping them from the total rainbow normally made by passing the white light through a prism.
The make up of our galaxy (which we now know thanks to spectroscopy is a conglomerate of smaller galaxies that collided long ago), our sun (which we now know had "parent" suns and even "grandparent" suns), and the elements of the universe writ large (which we know know is made of the same elements as the human body in near-direct proportion) are known. We know the universe's chemical composition from right here on earth thanks to the atoms of stuff absorbing certain, unique frequencies of light. And we know our place, chemically, in the universe since we see that we're made of the same stuff as everything else.
How does this impact society? Well, an unfortunately large portion of the population have NO idea about these ideas because they are not taught to people in high school (at least they were not presented to me). But it is important, in my opinion. In the (paraphrased) words of Dr. Neil Degrasse Tyson: We know we are in the universe, but we also know the universe is in us. Or Carl Sagan: "We are made of starstuff".
