An SVG is a Scalable Vector Graphic. Essentially it is just an image, but instead of being created with millions of tiny pixels, like a raster image (JPEG or PNG), they are made out of lines and points. This allows the image to be scaled up as large or small as you want, with out experiencing any quality loss (fuzziness/distortion) like you would see if you increased the size of a JPEG.
As you can see in this image, a vector graphic has a smooth outline, no matter how close I zoom in, or how large I make the image:
When you zoom in or enlarge raster image, such as a JPEG or PNG - you will see the tiny pixels that create the image:
SVGs are often used for cutting purposes with the Cricut/Cameo cutting machines, and probably what they are most known for. However, it is important to note, that while most cut files are in SVG format – not all SVGs are cut files.
Svgs are typically made out of fonts and simple graphics, however the fonts are converted to outlines, so it is no longer editable, in the sense of changing what it says.
They can also be used for basic printing purposes - or even use with Sublimation printers, and waterslide transfers.