To waive is to give up one's right to do something. If you waive your right to help name your family's new puppy, you can't complain if he ends up being called "Mr. Tinkerbell Sweetheart Lovey-Face."
Waive comes from a Middle English word meaning to abandon; the word waif, which refers to a neglected or orphaned child, shares the same root. However, while abandoning a child on a street corner is not okay, waiving one's right to do something is in most cases perfectly acceptable. A document stating one's decision to give up one's rights is appropriately called a waiver.