A transparent background means part of an image has no colour at all — instead of white or a solid box, you see whatever is behind it. This is essential for logos, product photos and stickers that need to sit cleanly on any page or design.
Only certain formats support transparency: PNG and WebP do, while JPG does not (which is why JPG logos end up with a white box).
You can create transparency by removing the background from a photo, then save it as a PNG. To make a round avatar, use Circle Crop.