Discolored Silicone Sealant

That black stuff is mold. You have to remove all the old sealant clean the area with bleach, dry and reseal with new silicone caulking. Moisture is causing the problem. After you make the repairs have a ventilation fan installed or open a window when using the shower. Also after bathing or showering wipe down the walls and that will greatly help in elimination the mold. I do that in my shower and never have soap scum or mold.