A charity scam is a fraudulent solicitation for a charitable contribution. It takes several forms, and the crude one, a charity that simply does not exist, is not the most common problem. A solicitation can be fraudulent while a real charity sits behind it, if what the donor is told about where the money goes is untrue.
Federal law is unusually specific about this. The Federal Trade Commission's Telemarketing Sales Rule provides at 16 CFR 310.3(d) that "it is a fraudulent charitable solicitation, a deceptive telemarketing act or practice, and a violation of this part for any telemarketer soliciting charitable contributions to misrepresent, directly or by implication," any of six kinds of material information: the nature, purpose or mission of the entity being raised for; that a contribution is tax deductible in whole or in part; the purpose the contribution will be used for; the percentage or amount of any charitable contribution that will go to a charitable organization or to any particular charitable program; any material aspect of a prize promotion, including the odds, the value, or that a contribution is required to win or to participate; and the organization's or telemarketer's affiliation with, or endorsement or sponsorship by, any person or government entity.
Two scope points, so the rule is not overstated. It governs telemarketing, which 16 CFR 310.2 defines as "a plan, program, or campaign which is conducted to induce the purchase of goods or services or a charitable contribution, by use of one or more telephones and which involves more than one interstate telephone call." And it binds a "telemarketer," meaning a person who initiates or receives calls to or from a customer or donor in connection with telemarketing. A door-knock or a purely postal appeal is outside this particular rule, whatever other law may reach it.
The related but separate question of how to check a charity before giving to it, from confirming its tax-exempt status to reading its financial filings, belongs to charity evaluation. This page is about the scheme and the law that names it.