IRS Publication 3833 (Rev. 9-2005) provides the following description of a charitable class:

The group of individuals that may properly receive assistance from a charitable organization is called a charitable class.  A charitable class must be large or indefinite enough that providing aid to members of the class benefits the community as a whole.  Because of this requirement, a tax-exempt disaster relief or emergency hardship organization cannot target and limit its assistance to specific individuals, such as a few persons injured in a particular fire.  Similarly, donors cannot earmark contributions to a charitable organization for a particular individual or family.  When a disaster or emergency hardship occurs, a charitable organization may help individuals who are needy or otherwise distressed because they are part of a general class of charitable beneficiaries, provided the organization who selects who gets the assistance.

Defining an appropriate charitable class is also critical in the Form 1023 exemption application.  Understandably, a new charity may initially benefit only a small number of individuals before it secures additional support to expand its provision of services.  However, the general charitable class to which the initial beneficiaries belong should be defined sufficiently to evidence a large or indefinite class and not a group of selected individuals.

For example, an organization limiting its beneficiaries to the class of 5 firefighters injured in a local disaster would not meet the requirements of a charitable class (because its benefits are limited to certain specific individuals).  In addition, contributions to charities earmarked to specific individuals do not qualify for a charitable deduction.  On the other hand, an organization which benefits local firefighters injured on the job now and in the future may benefit a sufficiently indefinite charitable class (because its benefits are not limited to certain specific individuals since the identities of future injured firefighters are unknown).

Of course, laws can carve out exceptions to the above restrictions.  For example, on December 21, 2006, President Bush signed into law H.R. 6429 which provides for an exception for payments made on behalf of any firefighter who died as a result of the October 2006 Esperanza incident fire in Southern California to any family member of such firefighter.  Five firefighters tragically died in the Esperanza fire.  Clearly, they would not constitute a charitable class, but Congress and the President gave the charity and its donors a pass (probably in large part because of the intense media coverage and public awareness of the event).