This classification of an organization as either a public charity or as a private foundation is important because different tax rules apply to the operations of these two categories.
For instance, private foundations are subject to excise taxes while public charities are not required to do so. Further deductibility of contributions to a private foundation is more limited than deductibility of contributions to a public charity. (See IRS Publication 526, Charitable Contributions for more details)
A 501(c)(3) organization is required to undergo a public support test every 5 years to prove that it is still a public charity, failing which their exempt status may be revoked.
An organization must prove that it has received at least 2/3rds of its funds from a variety of sources for the previous 5 years to pass the public support test.
Generally fiscally sponsored non-profit organizations pass the public support test. However organizations with just a few sources may not be granted permanent 501(c)(3) status. The public support test information is included in the 1023 IRS exemption application.