What’s the purpose of transparent background?

I use transparency for many reasons. When I'm creating complex composites with many layers stacked on top of each other, transparency allows bottom layers to show through top ones to create one cohesive image.

Also transparent PNGs are frequently used in web pages, apps and games.

A transparent background is not important if the image is going to be used on its own, as an entire rectangle. Then you don’t have to care about transparency.

A transparent background is essential and required if the image is not a perfect rectangle and you want to combine it with other images, like if you want to add it to a web page or a video. In the example below, if the star graphic (top left) has an opaque background, that makes it look very bad on top of a different background (top right). But if the star graphic has a transparent background (bottom left), then it can easily be combined on top of any other background (bottom right).

So, if you are watching TV and they put a non-square logo on the screen, the logo must have a transparent background or there will be an ugly rectangle around the logo on top of the video. If the designer did not make that logo background transparent, they might not get hired again.

The example below also shows you why they use a checkerboard. The checkerboard lets you know that a background is not solid white, it is transparent.

IMO a transparent background is not essential- It just acts as a base layer allowing every added image to 'float' and be re-positioned, re-sized, etc in the document. It could just as easy be a coloured background layer (useful as a 'Border' ).