My daughter has a hard pea sized solid bump at the back left base of her head. What is it?

A gland? At the base of the neck there are glands just like in the front of the neck. There are also many other possibilities so I would suggest you see your doctor to be sure exactly what it is.
Lymph node. It is likely an enlarged lymph node. These are fairly common. The lymph system is like arteries and veins but carry lymph which is like the waste and immune components (antibodies, etc)of our body and can get clogged or enlarged because of a small subclinical infection as part of our natural defense system. Always good to get checked out by doc, but not something urgent.