The right of first refusal is a term in contract law that gives its holder the option to enter a business transaction with the owner of something, according to specified terms, before the owner is entitled to enter into that transaction with a third party. In brief, the right of first refusal is similar in concept to a call option.
This related to family law in the child custody context. If there is a right of first refusal placed in your child custody order or parenting plan, this means that if the child is with you during your visitation or custodial time share and you cannot watch the child for a length of time, you are to call the other parent and give that parent the right to watch the child prior to getting a third person to watch the child.
The right of first refusal to watch the child can be worded many different ways and can be intended to reduce the need for day care services or to maximize the time the parents have with the children over none-parents.
The right of first refusal can create conflicts between parents too, and can be subject to modification if it is in the child's best interest.