Final answer:
The Supreme Court's decision in Miller v. California established that material is considered obscene if it meets all three parts of the Miller test: appeals to prurient interest based on community standards, depicts sexual conduct in a patently offensive way as defined by state law, and lacks serious value in literature, art, politics, or science.
Step-by-step explanation:
In Miller v. California, 1973, the Supreme Court ruled that material was obscene if (a) the average person, applying contemporary community standards, would find that the work, taken as a whole, appeals to the prurient interest, (b) the work depicts or describes, in a patently offensive way, sexual conduct specifically defined by the applicable state law, and (c) the work, taken as a whole, lacks serious literary, artistic, political, or scientific value.
These three criteria are collectively known as the Miller test, and they serve to determine whether a work should be considered legally obscene and not protected by the First Amendment. The application of this test can be quite complex, as it involves subjective judgments about both community standards and the value of the work in question.