Terrorism was originally defined in the Oxford English dictionary as "government by intimidation".
It has since then had a multitude of definitions, especially by governments intent on excluding themselves from it.
This wiki page on the subject gives a good overview.
In my opinion, Professor Pape's description is one of the most comprehensive:
"Terrorism involves the use of violence by an organization other than a national government to cause intimidation or fear among a target audience. Although one could broaden the definition of terrorism so as to include the actions of a national government to cause terror among an opposing population, adopting such a broad definition would distract attention from what policy makers would most like to know: how to combat the threat posed by subnational groups to state security. Further, it could also create analytic confusion. Terrorist organizations and state governments have different levels of resources, face different kinds of incentives, and are susceptible to different types of pressures. Accordingly, the determinants of their behavior are not likely to be the same and, thus, require separate theoretical investigations.
In general, terrorism has two purposes-to gain supporters and to coerce opponents. Most terrorism seeks both goals to some extent, often aiming to affect enemy calculations while simultaneously mobilizing support or the terrorists cause and, in some cases, even gaining an edge over rival groups in the same social movement (Bloom 2002). However, there are trade offs between these objectives and terrorists can strike various balances between them. These choices represent different forms of terrorism, the most important of which are demonstrative, destructive, and suicide terrorism.
Demonstrative terrorism is directed mainly at gaining publicity, for any or all of three reasons: to recruit more activists, to gain attention to grievances from softliners on the other side, and to gain attention from third parties who might exert pressure on the other side. Groups that emphasize ordinary, demonstrative terrorism include the Orange Volunteers (Northern Ireland), National Liberation Army (Columbia), and Red Brigades (Italy). Hostage taking, airline hijacking, and explosions announced in advance are generally intended to use the possibility of harm to bring issues to the attention of the target audience. In these cases, terrorists often avoid doing serious harm so as not to undermine sympathy for the political cause. Brian Jenkins captures the essence of demonstrative terrorism with his well-known remark, "Terrorists want a lot of people watching, not a lot of people dead."
Destructive terrorism is more aggressive, seeking to coerce opponents as well as mobilize support for the cause. Destructive terrorists seek to inflict real harm on members of the target audience at the risk of losing sympathy for their cause. Exactly how groups strike the balance between harm and sympathy depends on the nature of the political goal. For instance, the Baader-Meinhoft group selectively assassinated rich German industrialists, which alienated certain segments of German society but not others. Palestinian terrorists in the 1970s often sought to kill as many Israelis as possible, fully alienating Jewish society but still evoking sympathy from Muslim communities. Other groups that emphasize destructive terrorism include the Irish Republican Army, the Revolutionary Armed Forces of Colombia (FARC), and the nineteenth-century Anarchists." (Robert A. Pape (2003) The Strategic Logic of Suicide Terrorism, Source: The American Political Science Review , Vol. 97, No. 3, pp. 343-361)
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