Strict scrutiny is a form of judicial review that courts use to determine the constitutionality of certain laws. Strict scrutiny is often used by courts when a plaintiff sues the government for discrimination. To pass strict scrutiny, the legislature must have passed the law to further a "compelling governmental interest," and must have narrowly tailored the law to achieve that interest.
Strict scrutiny is the highest standard of review which a court will use to evaluate the constitutionality of governmental discrimination. The other two standards are intermediate scrutiny and rational basis review.
Strict scrutiny will often be invoked in an equal protection claim. For a court to apply strict scrutiny, the legislature must either have passed a law that infringes upon a fundamental right or involves a suspect classification. Suspect classifications include race, national origin, religion, and alienage.
The application of strict scrutiny, however, extends beyond issues of equal protection. Restrictions on content-based speech, for instance, are to be reviewed under the strict scrutiny standard as well. Notably, the Supreme Court has refused to endorse the application of strict scrutiny to gun regulations, leaving open the question of which precise standard of review is to be employed when addressing the Second Amendment.
For more on strict scrutiny, see this Catholic University Law Review article, this University of Vermont Law Review article, and this University of Pittsburgh Law Review article.