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The following is from IRS Source:  http://www.irs.gov/charities/article/0,,id=96104,00.html

For most organizations, an activity is an unrelated business (and subject to unrelated business income tax) if it meets three requirements:

1. It is a trade or business,
2. It is regularly carried on, and
3. It is not substantially related to furthering the exempt purpose of the organization.

There are, however, a number of modifications, exclusions, and exceptions to the general definition of unrelated business income.

Links
The IRS describes the special rules regarding UBIT here: Unrelated Business Income Tax. For more information, download Publication 598, Tax on Unrelated Business Income of Exempt Organizations.