When a couple with children gets divorced, the parent without custody (usually the father) is often ordered to pay a regular sum, known as child support, to the parent who retains custody of the children (usually the mother). The children need not be minors; for example, the noncustodial parent may have to pay a portion of his twenty-year-old child's college tuition. The amount of child support varies with the income of the parents; when I worked in family court, I saw amounts as low as $6/month (why bother?) and as high as $1000/week (the kid wasn't sick--what the heck was Mom doing with all that money?) Whatever the amount, the noncustodial parent can either pay the money directly to the custodial parent--in which case they have to trust that she won't falsely claim that she never received the money--or they can route it through a government agency, with all the bureaucratic hassle that involves.
Parents who fail to pay child support--so-called deadbeat dads--can suffer several consequences. In the simplest case, the child-support agency simply garnishes their wages, taking a set sum out of their paychecks each month. In some cases, these agencies can even garnish social-security, unemployment, or disability checks; I remember one father who threw a conniption fit when he discovered that the government was taking half his unemployment pay. (I wasn't terribly sympathetic. Hey, dude, you still created the kid; if you want to blame something, blame that organ a few feet below your mouth. And get a job). If the parent manages to avoid the garnish--say, by being paid under the table or hiding all his assets in his new wife's name--the agency can request a warrant for the parent's arrest.
Ordering arrest warrants was great fun, especially when I got to request one for someone who lived down the street from me. He had a nice new Porsche, a pretty house, and a new wife who wore lots of furs and jewelry; somehow, though, he couldn't manage to send a few hundred bucks to his ex. Curious, that. Jail shaped him up, though.
Child support serves as one step (but not the only step) towards enforcing parental responsibility--Dad helped create the child, so he should help support it. Moreover, it helps the custodial parent provide stable lives for her children--she shouldn't have to figure out how to live on half her previous income just because Dad decided he didn't want to be a dad anymore, nor should she avoid divorcing a violent or abusive husband just because she doesn't want to make life tougher for her kids.