Under eye veins? What is this veins purpose? (photos)

The discolouration is a normal consequence of a successful treatment. Time for the bruising to disappear will vary between patients but can take up to 6 month in some patients

The veins that you show serve no purpose and if they bother you then they can safely and easily be treated by many alternatives.

Thank you for your post.These are quite common and have no importnat role in normal physiology of the head and neck. They are related to thin skin, loss of fat as we get older, maybe sun damage (although I am not convinced of this).There are many ways to treat them including long pulse dye lasers. 

We see and treat these types of veins
quite frequently.  After a careful evaluation by an experienced
practitioner or physician, the veins under your eye can be treated with a certain type of laser.
It may take more than one treatment, but the results are very nice.I advise against filler to try
to correct this as it will lift the veins up and they may become more
noticeable. We have many veins in our body and can eliminate many
without any detrimental effects.