Now, on a more fundamental level than "it's cool to have a picture of a black hole," there are a ton of unresolved questions about fundamental physics that this result can shed a relatively large amount on. First of all, the entire event horizon is an insanely neat result predicted by general relativity (GR) to happen in extreme environments, so to actually see that is a great confirmation of GR. Beyond that, general relativity breaks down when so much mass is concentrated at a point that light cannot escape, in what is called a gravitational singularity, where you treat it as having infinite density when using general relativity. We don't think it literally is infinite density, but rather that our understanding of physics breaks down. (There are also several secondary things we don't understand about black hole environments, like the mechanism of how relativistic jets get beamed out of some black holes.) We are literally talking about a regime of physics that Einstein didn't understand, and that we can't test in a lab on Earth because it's so extreme, and there is literally a booming sub-field of theoretical astrophysics trying to figure out these questions. Can you imagine how much our understanding of relativity is going to change now that we actually have direct imaging of an event horizon? It's priceless!
Third, this is going to reveal my bias as a radio astronomer, but... guys, this measurement and analysis was amazingly hard and I am in awe of the Event Horizon Telescope (EHT) team and their tenacity in getting this done. I know several of the team and remember how dismissed the idea was when first proposed, and have observed at one of the telescopes used for the EHT (for another project), and wanted to shed a little more on just why this is an amazing achievement. Imagine placing an orange on the moon, and deciding you want to resolve it from all the other rocks and craters with your naked eye- that is how detailed this measurement had to be to resolve the event horizon. To get that resolution, you literally have to link radio telescopes across the planet, from Antarctica to Hawaii, by calibrating each one's data (after it's shipped to you from the South Pole, of course- Internet's too slow down there), getting rid of systematics, and then co-adding the data. This is so incredibly difficult I'm frankly amazed they got this image in as short a time as they did! (And frankly, I'm not surprised that one of their two targets proved to be too troublesome to debut today- getting even this one is a Nobel Prize worthy accomplishment.)