In order for solicitation to take place, the person requesting the criminal activity must have the intent that the crime actually be committed or the intent to engage in the criminal activity with that person.
The most common form of the crime is the solicitation of prostitution - offering money to someone to have sex. But solicitation can be committed for any crime, such as murder or arson.
The actual crime does not have to take place in order for someone to be charged with solicitation. As long as the request was made and compensation offered, the crime of solicitation has taken place, whether or not the person follows through on the criminal behavior.