Solicitation (when used as a legal term) refers to the act of offering sex in exchange for money, or offering money in exchange for sex. In the UK, prostitution itself is not a crime, but soliciting in a public place is.

I, as usual, agree with the BritishEnglishCoach! However, you should also know that offering the act of sex for money, prostitution, is not the only legal use of solicitation, albeit the most commonly used one. Any time someone asks another person to commit any crime, the act of asking is the crime of solicitation.