Short answers, pulled from the story.
Common law is a body of law developed primarily through judicial decisions rather than statutes, relying on the principle of stare decisis, meaning courts follow precedents established in previous similar cases. Statutes are generally understood to supersede common law, and legislatures may codify or overrule it, but common law remains the primary source of law in areas such as contract law and the law of torts.
Common law originated in the practices of the courts of the English kings in the centuries following the Norman Conquest in 1066. Henry II, who became the first Plantagenet king in 1154, institutionalized it by creating a unified court system, sending itinerant judges throughout England and establishing a body of decisions that became binding precedent.
The law of the state of New York is frequently chosen in commercial contracts because of its depth and predictability, built up through New York's history as the United States' commercial center. Delaware corporate law is similarly chosen for merger, acquisition, and shareholder agreements because of the dense body of corporate case law Delaware has accumulated over time.
Approximately one-third of the world's population lives in common law jurisdictions or mixed systems that integrate common law and civil law. Countries using common law include Australia, Bangladesh, Canada, Ghana, India, Ireland, Israel, Kenya, Malaysia, New Zealand, Nigeria, Pakistan, Singapore, South Africa, the United Kingdom, and the United States, among many others.
Stare decisis, meaning "to stand by things decided," is the doctrine that courts follow precedents established in previous decisions involving similar facts. In the United States federal system, decisions of a circuit court of appeals are binding on district courts within that circuit, while decisions of one circuit are only persuasive authority in other circuits; the Supreme Court, which always sits en banc, can overrule its own prior decisions.
Common law systems place great weight on judicial precedent as a source of law and use an adversarial system where two sides present their cases to a neutral judge. Civil law systems, used in Continental Europe, Mexico, and much of Latin America, trace their lineage to Roman law and the Napoleonic Code; they traditionally give less weight to judicial precedent, and the Napoleonic Code expressly forbade French judges from pronouncing general principles of law.