The term "obscenity" refers to anything that offends people's morals. However, the term is generally used to refer to things that are offensive in a sexual way. In other words, a depiction of someone stealing would offend our morals, but it would not be obscene. The word has come to be connected mainly (especially in E-commerce) with pornography.
In the United States, at least, it is very hard to clearly define what is and is not obscene. In the case of Miller v. California, the Supreme Court set up a three-part test to define obscenity. They said that something is obscene if it
- appeals to "the prurient interest"
- depicts sexual conduct in a "patently offensive way" and
- lacks (as a whole) and "serious literary, artistic, political, or scientific value."
As you can see, this is a very vague rule. "Prurient" refers to an "excessive" or "unhealthy" interest in sex. This is hard to define. It is hard to say what is "patently offensive." It is also hard to define "serious....value." Therefore, it is very hard to define what things are and are not obscene, at least in the US.