If the body part name in the sidebar is red, you’re bleeding and need to bandage to stop the bleeding. If you’ve stopped the bleeding, the name will turn white again.
If the body part is shown in blue, you’ve got a deep bite which could get infected and you need to disinfect it. If you’ve successfully disinfected it, the body part name will turn white.
Beyond those two situations, wounds will heal without bandages or disinfecting at a rate based on your traits (fast healing, slow healing, etc.), but it can take a while, especially if you or a slow/imperceptible healer. But bandaging will make them heal quicker, with various qualities of bandaging effecting how much faster they heal. Also, disinfecting will make them heal faster, also dependent on the quality of the disinfecting.
Bandaging quality depends on the bandage used and on first aid skill. Real bandages (like from first aid kits) are better than bleached/boiled makeshift bandages, which are better than plain makeshift bandages, as you might expect (not sure if bleached or boiled is better, or if there is a difference). Disinfecting depends on first aid skill. It might also depend on what you disinfect with, but I always use the stuff in the first aid kits. Cattail jelly can also be used, but I’m not sure how it compares.
That’s all I have to say about that.