Solicitation is a crime; it is an inchoate offense that consists of a person inciting, counseling, advising, urging, or commanding another to commit a crime witht the specific intent that the person solicited commit the crime. It is not necessary that the person actually commit the crime.
For example, if A commands B to assault C and A intends for B to assault C, then A is guilty of solicitation. However, if A commands B to assault C without intending that an actual crime be committed (perhaps believing that C has given consent), then there is no solicitation.
Solicitation is also subject to the doctrine of merger, which applys in situations where the person solicited actually commits the crime. In such a situation, both A and B could be charged with the crime as accomplices, which would preclude conviction under solicitation. a person cannot be punished for both solicitation and the crime solicited.
Note that Solicitation can apply to just about any criminal act. There are also many statutes for specific solicitation crimes. For example, solicitation of murder is often considered a capital offense, and has its own statute. Another example might be solicitation of prostitution.
See also