501(c)(3) refers to a section of the U.S. federal income tax code. Organizations that have been granted 501(c)(3) status by the Internal Revenue Service may only conduct non-partisan activities. 501(c)(3) groups are sometimes referred to as "non-profits." This can be a source of confusion, since all U.S. states allow certain corporations to register as "not-for-profit" corporations. A corporation may be a not-for-profit corporation under the laws of the state in which it is incorporated, but not have federal 501(c)(3) status.
Donations to 501(c)(3) groups are tax deductible for the individual who makes the donation. 501(c)(3) organizations are not required to publicly disclose their donors. They may choose to do so, or the donor may choose to disclose that he or she provided a grant to a 501(c)(3) organization.
Some non-profit groups have two related corporations -- a 501(c)(3) and a 501(c)(4). Under IRS tax code, it is legal to transfer funds from a 501(c)(3) to a 501(c)(4), but the restrictions on how the money is spend carry over on any such transferred funds.