In 1973, a narrow majority of the Court sought to end nearly two decades of being up to its ears in obscenity cases by adopting what it thought was a narrow, workable and and broadly palatable definition of obscenity. The three-prong Miller v. California test controls to this day; it asks:
(a) whether the average person, applying contemporary community standards would find that the work, taken as a whole, appeals to the prurient interest; (b) whether the work depicts or describes, in a patently offensive way, sexual conduct specifically defined by the applicable state law; and (c) whether the work, taken as a whole, lacks serious literary, artistic, political, or scientific value.
Ever since Justice Douglas's dissent in Miller, its opponents have argued that the test is impermissibly vague. But the Court rebuffed this concern:
Under the holdings announced today, no one will be subject to prosecution for the sale or exposure of obscene materials unless these materials depict or describe patently offensive "hard core" sexual conduct specifically defined by the regulating state law, as written or construed. We are satisfied that these specific prerequisites will provide fair notice to a dealer in such materials that his public and commercial activities may bring prosecution.
The Court has repeatedly rejected vagueness concerns about the Miller standard ever since. In doing so, it has consistently pointed to the phrase "sexual conduct specifically defined by the applicable state law." Under this prong, state laws must spell out the particular things or acts that are subject to the obscenity law. For example,
actual or simulated sexual intercourse, deviate sexual intercourse, sexual bestiality, masturbation, or sadomasochistic abuse; actual lewd exhibition of the genitals; actual physical contact with a person's clothed or unclothed genitals, pubic area, buttocks, or, if such person is a female, breast with the intent to arouse or gratify the sexual desire of either party; or any act or conduct which constitutes sexual battery or simulates that sexual battery is being or will be committed.
That's plenty specific enough - if all you needed to know was not to include any of the above in your work, you'd be set. But there's more to Miller than that. The table below illustrates the remaining vagueness problem:
What's in Box C?
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With specified conduct
Without specified conduct
Prurient, offensive & no serious value
Non-prurient, non-offensive, and/or has serious value
When the "sexual conduct specifically defined by state applicable state law" aspect of Miller is separated out from its other components, all speech can be divided into the above four groupings. Only one grouping is illegal: speech in Box A meets all parts of the Miller test. When the Court rejects vagueness arguments about Miller, it is talking about the Y (vertical) axis of this table: you know where you stand with Box B and D, because they lack the specifically defined sexual conduct. As long as you stay on the right side of the Y axis, it doesn't really matter whether your speech actually falls in B or D, because either way you're safe.
But suppose you want to do something that does involve the specifically defined sexual conduct. As long as your speech is in Box C and not Box A, it is your constitutional right to do so. And here you run smack into the vagueness problem: the Y axis may be a bright line, but the X axis - the line that separates the constitutionally-protected C from the criminal A - remains blurry. Once your are on the left side of the Y axis, all that specific definition is cold comfort.
Effectively, the specific statutory definition of "sexual conduct" provides a safe harbor, so you can avoid risk by making sure you stay inside that line. This wouldn't be a problem if we were talking about a commercial regulation. But in the realm of speech, this is called a chilling effect, and it is generally impermissible. Sure, individuals know how not to break the law. But they don't know how to exercise the full extent of their First Amendment rights while not breaking the law. Box C is constitutionally protected speech, but that blurry horizontal line counsels you to get back over into B or D.
This is the vagueness problem: speakers who would like to be in Box C are chilled, even though Box C is constitutionally protected.