The darkness of armpits could be that dead skin cells have built up but this is an easy fix. Just exfoliate the armpits. You can choose natural exfoliants such as sea salt and/or one that contains lactic acid such as yogurt or a manufactured product.
Also, it could be the applied product. Some people claim that their armpits become darker from using a particular shaving cream, deodorant, etc. So, using a different brand or decreasing the use of the product in question may help if the skin is reacting to a particular ingredient. My friend only uses deodorant manufactured by Tom’s for this reason.
Last but not least the darkness could be a result of hair stubble. Since the hair stubble and ingrown hair is dark it creates a dark shadow (so to speak). So, if shaving is not eradicating the dark shadows then try waxing your armpits. Waxing will pull the hair out as opposed to shaving that sometimes leaves behind a very small amount of hair above the skin.
Okay, waxing isn’t your thing-too uncomfortable. Try using creams such as Nair or Veet that are used in place of shaving hair.