What are spider veins?

You have noticed fine marks on the skin of your leg, and you want to know whether they are spider veins before you decide what to do about them.
The plain definition
my.clevelandclinic.org defines them this way: Spider veins are damaged capillaries, venules and arterioles (small blood vessels) that look red, blue or purple.
Using that description
The words to hold on to are small blood vessels and red, blue or purple. Use them to describe what you see to a clinician instead of guessing at the name.
Four pages around this one
Four pages cover the ground around this one: the venous disease overview, the varicose veins guide, the spider veins guide and the MedlinePlus page on varicose and spider veins.
The question to take with you
Ask the clinician to confirm what you have rather than assuming. "Are these spider veins, and is anything else going on in my legs?" is a fair question to put before you agree to treatment.