What adoption is:
Adoption is the legal act of taking parental responsibility for a child whose original parents are unable to fulfill that responsibility.
Who can adopt?
The government requires that the adoptive parents undergo a complete background check. An assessor (usually a representative from a state adoption agency, or a licensed social worker) visits prospective parents’ homes and interviews all of the family members within the household. A complete history is taken of each family member, especially in reference to criminal history, medical history, mental history, abusive history, religious beliefs, education, financial stability, and income. All of these factors contribute to the assessment of each prospective family that is written up in a report given to the court, which makes the final call on whether the prospective parents are fit for adopting. 
Laws concerning Consent
In all states, consent must be gained from the birth mother and the birth father if his identity is known. In most states, the father must give his consent to the adoption. There are a few circumstances in which the birth parents may lose their rights as parents, such as if they are deemed unfit parents due to abuse or neglect.
Consent must be written and notarized or written in court. In almost all states, consent for adoption is not legally binding until after the child’s birth, which gives the parent(s) the option to revoke consent up until the child is born when final consent is given.
Consent must also be given by any Adoption agency involved, especially that which investigated and interviewed the prospective adoptive parents. Also, the prospective parents must consent to the adoption of the child and the legal responsibilities this entails.
Adoption is meant to be a permanent placement of a child in a safe environment. Because of this desire to create as stable of a situation for the child as possible, the ability for a birth parent to revoke their consent of adoption is fairly limited. Depending on what state you are in, there is may be an initial window of opportunity for the birth mother to change their mind right after the adoption has taken place and before the consent becomes final. In many states this window is 10 days, but can be as high as 60 days in some states. If you have further questions you should ask a lawyer or look at the specific laws in your state.