A vector file is a type of digital image that is created using mathematical equations and geometric shapes. Unlike photos or other types of images, vector files don't lose quality when you resize them, making them perfect for things like logos and illustrations. Imagine if you had a logo for your business, and you needed to put it on everything from business cards to billboards. With a vector file, you wouldn't have to worry about the logo looking fuzzy or pixelated, no matter what size you needed it. That's why many companies use vector files for their branding and marketing materials.
See: What is the difference between a vector and raster file?