Vector graphics are magical. Hey, I'm serious! Have you ever tried to enlarge a graphic, and it started to look grainy or pixelated? That's because it wasn't a magical vector. Let's talk about the vector magic and why it matters.
Vector graphics use magical math (that I don't claim to understand) to represent an image. And because they use this magical math, it means that they can be enlarged or reduced without losing image quality. Vector files end in extensions like .eps, .ai, and .svg. On the other hand, raster graphics use a grid of pixels to represent an image. That's why when you start to enlarge a raster image, you begin to be able to see those pixels and your image quality becomes poor. Examples of raster image files are the familiar .jpg and .png file formats you've probably seen before. (If you want to know more about vectors and rasters, the Great Wiki would be happy to help you here and here.)
So why would you ever want anything other than a magical vector graphic then? Well, vectors are only magical in certain places. You see, in a design program like Adobe Illustrator or Affinity Designer, vectors rule the land! But online, pretty much anything can display a lovely raster graphic, while vectors...not so much. So vectors are often used in the creation of designs and then exported to a raster format for display online.
Take, for instance, the case of logo design. When I make a logo for a client, I use vectors to create the logo. Since I know that the client will need varying sizes of logo for different uses, like their website, social media, business cards, email, etc., I resize the vector graphics and then export them at various raster sizes for the client to use in those assorted locations. I also give the client a copy of their vector logo so that they have the editable version of the design if they ever need it in the future.
So will you use vector images in your business a lot? Well, unless you are in the field of creating images or designs, probably not. But it's a very good thing indeed to know what vector graphics are and to make sure that you always get that magical, editable vector copy of your graphic from anyone who does image design work for you. Then all you need to do is bibbidi, bobbidi, boo that vector copy to someone with a design program if you need to make any changes down the road.