Absent a specific law, an inchoate offense requires that the defendant have the specific intent to commit the underlying crime. For example, for a defendant to be guilty of the inchoate crime of solicitation of murder, she must specifically intend to cause the death of a particular human being. It would not be enough for Defendant to ask another to kill the victim when she simply intended to scare the victim. (Note that specific intent can be inferred, and many people would infer the specific intent to kill the victim simply by Defendant asking another to do it).
There can be various causes of failing the commission of the underlying crime, for example arrest prior to committing the crime, accident which prevents the crime, or even impossibility. For example, Defendant takes a gun that he believes is loaded, points it at victim, and with the intent to kill victim pulls the trigger. The gun is not loaded however, and victim runs away. In this case Defendant would be guilty of the inchoate crime of attempted murder even though it was actually impossible for Defendant to commit the underlying crime, here murder.
Examples of inchoate offenses include conspiracy, solicitation, and attempt, as well as some public health crimes.
See also: criminal law