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.

If you want to import some transparent images to your GIF animation, you can do so using the File > Open as Layers option. In case you have images with a solid background but you want to add them ...

Making the background transparent – sometimes referred to as "punching out the background" by graphic artists – is a straightforward task in Adobe Photoshop.