A more thorough explanation:

Abstention is a legal doctrine that prevents federal courts from hearing cases within their jurisdiction and instead gives state courts authority over the case. This doctrine is based on federalism and allows state courts to adjudicate matters that are of particular significance to the state or its laws. Conflicts surrounding abstention commonly arise out of constitutional challenges to state laws.

The abstention doctrine can be further divided into various sub-doctrines, based on a number of Supreme Court cases that have expanded on when abstention is warranted. These cases include:

• The Pullman Doctrine: Federal courts should exercise discretion to stay from a case when state court proceedings can resolve the issue.
• The Younger Doctrine: Federal courts should abstain from cases that are pending in state proceedings.
• The Burford Doctrine: Federal courts should defer to state courts to review the state's agencies.
• The Rooker-Feldman Doctrine: Lower federal courts may review the constitutionality of state-promulgated statutes and rules, but they may not review holdings of the state's supreme court pertaining to those policies.

Here are some examples of how these sub-doctrines work:

• The Pullman Doctrine: A federal court may abstain from hearing a case challenging a Texas law that implicates violations to the Fourteenth Amendment. The court may instead allow the Texas Supreme Court to interpret the state law and resolve the issue.
• The Younger Doctrine: A criminal defendant may challenge the constitutionality of a California criminal statute in federal district court while their criminal case is pending in state court. However, the federal court may abstain from hearing the case and allow the state court to resolve the issue.
• The Burford Doctrine: A federal court may refuse to hear a case challenging a state agency's decision and instead defer to state courts to review the agency's decision.
• The Rooker-Feldman Doctrine: A federal court may review the constitutionality of a state's bar rules promulgated in non-judicial proceedings. However, the court may not review holdings of the state's supreme court pertaining to those policies.

These examples illustrate how the abstention doctrine works in practice and how federal courts may abstain from hearing cases in certain circumstances.