Type of graphics

In this context, there are essentially 2 types of images: a vector type and a raster type.

A vector image does not store any pixel information. Instead, it stores equations of lines and curves, and a program (like Illustrator) can interpret those curves and draw accordingly. This is nice because you can scale arbitrarily large without losing resolution. However, you will need the code that can interpret this format, which to my knowledge, Unity doesn't have. In addition, there will be no way you can use this type of image as a texture unless you convert it to a rasterized image. Unity might have this conversion feature, but most vector based software would have raster output too.

A raster image stores an array of pixels. Most image formats (png, etc) are raster based. The good thing about these types of images is that they are easy to draw, and you can pass the array to the graphics card and use the image as a texture. Since raster images are just pixel arrays, you can't scale them without having to do extra work. Fortunately, Unity does have multiple ways of interpolating/filtering images when you scale them so this shouldn't be a problem. For most games, you would want to use raster based graphics because they're simple to work with.