As popularized by Milhouse on The Simpsons, a phrase referring to the father of a child who's parents are divorced and split custody of the child.

In such situations, what can happen is the mother has custody of the child during the week, while the father gets to spend one or both days of the weekend with him or her.

Phrase is especially true if the mother is remarried or has a boyfriend, hence the child's father figure during the week. This makes the biological father the weekend dad.

When you eat dirt for the first time and leave your family to build a shack in the woods

A politically correct rewording. The original term was/is "Weakened Dad" which is loosely based on a spouse or former spouse's actions toward her child's father.