Contempt of court is the strongest remedy for obtaining child support from a recalcitrant obligor. In short, if an obligor disobeys a court order to pay child support, the obligor can be fined, punished by a jail term and imprisoned until he does pay the child support - all at the same time. Usually, courts order obligors imprisoned until they pay. For this reason, it is often said that the obligor holds the keys to the jail in his own hands.
Contempt of court is said to be civil or criminal, or both. If a judge puts a person in jail until he pays his child support, or some part of it, then it is considered civil contempt. If a judge puts a person in jail for a certain period of time whether or not he pays his child support, then it is considered criminal contempt because the purpose is punishment, not coercion into paying child support.
When a person receives a summons, subpoena or similar process to attend a child support hearing, but then fails to show up, the judge has the power to issue a bench warrant that the person be arrested and then brought before the court so that the hearing can go on. This isn't criminal - it's just the court enforcing its power to compel people to appear and testify.
None of the above is considered "criminal" in the same way that committing a felony is criminal. But one can be criminally prosecuted for failing to pay child support. Normally district attorneys do not prosecute people under the criminal law unless they owe a lot of money and have had many opportunities to pay.
Contempt is a complex matter. Often judges and attorneys have trouble figuring out whether contempt is civil or criminal (or both) in nature.