This phrase comes from Latin and means something like “let the decision stand.” It is a general principle of law in the United States as well as in other countries. What it means is that once a court decides a case, its decision will be honored by all other courts trying similar cases. This is especially likely to happen if a court of last resort (like the Supreme Court of the United States) makes a decision.
The idea behind stare decisis is that it is good if people can know what the law is. If they are trying to decide what the law is, they should be able to look up court cases dealing with similar issues and have a reasonable certainty that a court will rule the same way in their case. When courts follow precedents set by previous courts, this certainty exists.
Of course, stare decisis is not an ironclad rule. For example, when the Supreme Court ruled on the case of Brown v. Board of Education in 1954, it did not abide by the precedent set in 1896 in Plessy v. Ferguson. Instead, it broke from the idea of stare decisis and made a new precedent.
Stare decisis, then, is the idea that courts should generally rule in ways that are consistent with what courts have ruled in the past.