A birth father is a man who has fathered a child and then placed that child up for adoption.
It is important to remember that not only does the potential birth mother have rights regarding the decision to place their child for adoption, but so does the potential birth father. Even if the birth father is no longer a part of the birthmother's life, or even listed on the birth certificate, that potential birth father has just as much right as the potential birth mother. If the potential birth mother does not know who the father of the child is, his rights still need to be addressed somehow, in most states. Whether the pending adoption is a step parent adoption, a private or public adoption - either consent has to be given or termination of rights must take place prior to finalization of adoption.
Each state has laws regarding the terminating, or relinquishment of parental rights of the birth mother and birth father. Some states require legal notice be given to the birth father of a proposed adoption, other states don't require notification, while some states state that if a birth father is not registered with the state putative fathers registry, that they don't need to be notified. Some states require an advertisement in some form of pubic media to notify the birth father and protect his rights and if no one comes forward then it is assumed that the adoption can proceed. Some of the grounds for terminating the birthfathers rights through legal recourses are: severe abuse or neglect, abuse or neglect of other children in the household, abandonment, long term mental illness, failure to support or maintain contact with the child or a felony conviction for a crime of violence against the child or other family member and finally for being incarcerated for a length of time that would be detrimental to the child.
Nearly half the states in the U.S. have statues that allow the establishment of putative father registries where the father can register or acknowledge paternity within certain a certain timeframe which will allow him to be notified in case a child he has fathered might be put into an adoption situation.
If the birth father is with the birth mother and they have decided to make an adoption plan together, then a consent to adopt document is all that is needed in most states. Some states allow this to be done prior to the child being born, while other states only allow it to happen after the birth of the child.
An ethical adoption social worker or adoption attorney will try to get as much information as possible about the potential birth father and not only try to protect his rights as well as being able to obtain information from him about his medical and genetic background.