There are two main file type categories for image files, being "Vector" and "Raster".
Most people are probably more used to Raster images, which are basically big grids of thousands of tiny little coloured squares(called pixels), which when all put together, make an image. These are commonly found in JPG, PNG and GIF file types and are what you're dealing with when using programs like Photoshop or Paint.NET.
Vector files are the less common image type of the two, and vector files are images made up of shapes, lines, and points all moulded together to make logos, designs and photos. These are usually saved as .EPS, .PDF, .AI or .SVG files, and these are what you're dealing with when using programs like Illustrator or CorelDRAW. Odds are, if you went through a professional designer for your logo, you probably have a vector file.