What would cause a neck mass in a 3 year old?

Lots of things.: Causes range from enlarged lymph node, cyst, abscess, enlarged thyroid, and scar tissue, to a tumor. It's best to have the doctor evaluate it.

Many possibilities: Neck masses in children are common, and much less likely to be cancer than in adults. Infectious causes are common. If it is persistent for more than a few weeks, or painful, or red, or causing other problems, then the child should see their doctor quickly.