We'll look at two ways to make the background transparent: an automatic approach which only takes a few seconds, but might fail when used on complicated images, and a manual approach you can try ...

When you try to save such an image, the background area of the image will no longer be transparent and turns into solid color; in most cases, white i.e. Color 2.

To make Background Transparent in Photoshop, you can use Selection tools, Magic Wand, Select and Mask. Read more in this post.