Se refiere a lesiones o daños causados por difamación, injurias, violación de la privacidad, apropiación indebida de ideas, etc.

Te copio varios links y definiciones que he encontrado:

http://www.coverageglossary.com/explanations/ltr604.htm
ADVERTISING INJURY LIABILITY
"Advertising Injury" means injury rising out of an offense committed in the course of your advertising activities, if such injury rises out of libel, slander, defamation, violation of right of privacy, piracy, unfair competition or infringement of copyright, title or slogan.

Advertising Injury
Damages or injury sustained by a claimant in the course of the advertising activities of the insured which included such injury as libel, slander, violation of the right to privacy, misappropriation of advertising ideas, or the infringement of copyright.

Advertisers Liability Insurance
Covers an insured against claims for libel, slander, defamation, infringement of copyright, invasion of privacy, etc., arising out of its advertising program. Also available for radio and television stations and advertising agencies.

http://www.gordonrees.com/cites/40f3d968.cfm
(...) In essence, advertising injury was defined under the policies as injury occurring in the course of Microtec's advertising activities if the injury arose out of defamation, invasion of privacy, piracy, unfair competition, or infringement of copyright. The coverage excluded advertising injury arising out of breach of contract, infringement of trademark and wrong description of goods. (...)

De no encontrar la traducción exacta, sugeriría traducir la definición:
"Daños causados durante la actividad (campaña) publicitaria, ocasionados por difamación, invasión de la privacidad, etc."
O tal vez un poco más resumido, ya que se trata de una lista.

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Note added at 3 hrs 29 mins (2005-08-16 23:09:00 GMT)
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http://insurance.cch.com/rupps/advertising-injury-coverage.h...
Advertising Injury Coverage
Coverage for advertising injury provided by the commercial general liability policy under coverage Part B and by some umbrella policies. Advertising injury is a statement made in the course of advertising activities that causes loss to another person or business by libel, slander, defamation, violation of a right of privacy, piracy or misappropriation of ideas, or infringement of copyright, trademark, title or slogan. Coverage can also be purchased as a separate advertiser\'s liability policy or as an endorsement to another business policy form.

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Note added at 3 hrs 32 mins (2005-08-16 23:11:37 GMT)
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http://insurance.cch.com/rupps/advertising-injury-coverage.h...
Advertising Injury Coverage
Coverage for advertising injury provided by the commercial general liability policy under coverage Part B and by some umbrella policies. Advertising injury is a statement made in the course of advertising activities that causes loss to another person or business by libel, slander, defamation, violation of a right of privacy, piracy or misappropriation of ideas, or infringement of copyright, trademark, title or slogan. Coverage can also be purchased as a separate advertiser\'s liability policy or as an endorsement to another business policy form.