These sponge-like thingies can often be seen in Asian countries. They are actually a protection that comes from the manufactures. Attached to the doors, they help to keep paint intact during transportation. Some people like to keep them, especially if they live in heavily congested areas with tight parking spaces. So in short, the blue sponge is a protection from dents or paint damage.
If you fancy having them on your car and blue is not your favorite color, then there’s a variety to choose from online.
Personally, I wouldn’t put them on my car but you do you.