common law marriage came about through just that, English common law, or law “for the commons” (people not the nobility) which developed gradually out of Anglo-Saxon law, evolving through the Norman and subsequent periods. It is the foundation of our own legal system, and at one time anything that was not covered by a specific statute (statutory law is in a way the opposite of common law) was governing by precedents of common law. In that concept, a common law marriage recognized that after a due period of time cohabiting, esp. if children resulted, the consent of the two parties was enough to establish civilly valid marriage.
Read Regency romance novels and you will find the couples elope head for Gretna Green, the first town over the Scottish border, where consent of the parties, without civil or church witnesses, was enough to establish marriage. Several states (Texas among them) still recognize common law marriage, but differ in what is necessary to establish it, usually the minimum is mutual consent and holding themselves out to the public as a married couple. It is important because of child custody and property rights, and the effect on divorce laws. In most states, statue has taken over the regulation of marriage, and of other areas formerly covered in common law, but it may still be cited by lawyers as legal precedent in some cases.