Binding precedent refers to existing law that must be followed. Such precedent exists within common law jurisdictions that recognize judicially made law. Generally, it follows the doctrine of stare decisis, which means "maintain what has been decided and do not alter that which has been established."
Certain countries and jurisdictions follow a common law system of law. For example, England and most states within the United States, with the exception of Louisiana, use this type of system. It is an alternative to a civil law system, which is used by other countries including France.
In a common law system, when a judge makes a ruling on a case, that ruling becomes the law. For example, if a judge presiding over a contract law case says that the parties signing the contract have a duty to read before they sign, then it becomes the law that any parties signing a contract have a duty to read it. Judge made law, also called common law or case law, is the law and remains the law unless the state or federal legislature passes a different rule changing the common law. Judges can also define laws passed by the legislature, and those definitions and interpretations also become the law.
All of the body of law made by the judges is referred to as precedent. Only some precedent, however, is binding precedent. Whether precedent is considered binding or not depends on who made the rule.
There is a hierarchy of courts within the US: courts of appeals, for example, are higher in importance than local courts in most states. Supreme courts are the highest court of all, except in New York where the Supreme Court is the lowest court. When a higher court makes a ruling, it is binding on all courts at that level and lower. For example, if the Supreme Court makes a ruling, it is binding on appellate courts.
Each state and the federal government also have their own court systems. A state court ruling is only binding precedent on other courts at or below its level within the state. A federal court ruling is only binding precedent on other courts at or below its level on the federal level. If the Supreme Court of the United States makes a ruling, it is the highest court of all and is considered binding precedent on any and all other courts within the United States.