What is the full faith and credit clause?

The "full faith and credit clause" refers to a provision in article 4, section 1 of the Constitution of the United States. In simple terms, the clause means that state courts must respect the judgements of courts in other states. This was a way for the framers to ensure that states' rights must be given their due and are properly enshrined under the Constitution. The clause was also considered useful as a means of settling disputes between neighboring states.
Today, the clause's main use relates to family law. For instance, many states now legally recognize same-sex marriages and adoptions by same-sex couples. Yet other states do not. That being the case, it has become increasingly necessary for the Supreme Court to intervene in order to settle disputes. In the case of V.L. v. E.L. (2016), for example, the court ruled that the state of Alabama, which did not permit gay couples to adopt, nevertheless had to respect the plaintiff's rights under Georgia law, where adoption had originally been granted.
 
https://legal-dictionary.thefreedictionary.com/Full+Faith+and+Credit+Clause