The defining characteristic of twisting is the use of deception to sell a policy. There's nothing wrong with an insurance agent encouraging prospective clients to replace their current coverage with a policy from the company the agent represents -- provided that the new policy actually does a better job of meeting the client's needs. In twisting cases, however, it typically isn't in the client's best interest to take out a new policy. That's why the agent has to deceive the client by "twisting the truth," which is how the practice got its name.
Life insurance often presents opportunities for twisting. Suppose a person has a whole-life policy with an accrued cash value. An insurance agent tells this person that he can reduce his premiums by canceling that coverage and taking out a term policy --
but the agent doesn't mention that doing so may cause the client to forfeit the cash value or pay taxes on it, wiping out any savings from the premiums. Another example might be an agent encouraging a potential customer to replace her existing health coverage with a policy that's cheaper but that the agent knows won't cover her medical conditions, setting her up for a potential financial catastrophe down the road.
The National Association of Insurance Commissioners has produced a model law, called the "Unfair Trade Practices Act," which prohibits agents from misrepresenting any aspect of insurance policies, thus making twisting illegal. Most states have enacted this model law. Many states also have laws that specifically define twisting as a criminal offense. Even in the absence of such laws, twisting could be prosecuted under general fraud statutes.