Transparency is possible in a number of graphics file formats. The term "transparency" is used in various ways by different people, but at its simplest there is "full transparency" i.e. something that is completely invisible. Only part of a graphic should be fully transparent, or there would be nothing to see.
What does transparent background do?
A PNG is an image file type that allows you to have no background color. Most images cover a certain number of pixels and have color in all of those pixels, even if that color is white. A transparent background has nothing in the background pixels, allowing what's behind it to show through.
How do I make my background transparent?
You can create a transparent area in most pictures. Select the picture that you want to create transparent areas in. Click Picture Tools > Recolor > Set Transparent Color. In the picture, click the color you want to make transparent.