First, there is the Webster’s definition:
the systematic use of terror especially as a means of coercion
Of course there is the heavy reliance on the root, “terror,” but note also the inclusion of the word “systematic” in the definition.
More important to discussions of whether or not certain acts involving US citizens are or are not acts of terrorism are the definitions used by the Central Intelligence Agency (and other members of the US Intelligence Community):
the term “terrorism” means premeditated, politically motivated violence perpetrated against noncombatant targets by subnational groups or clandestine agents
and the Federal Bureau of Investigation (FBI):
Terrorism includes the unlawful use of force and violence against persons or property to intimidate or coerce a government, the civilian population, or any segment thereof, in furtherance of political or social objectives.
Although the definitions vary based on the focus of each agency, and the FBI concedes “there is no single, universally accepted, definition of terrorism,” both require knowledge of the motivation for the particular act. Without knowing why a person or group carried out an act of force or violence, it is impossible to determine whether it was terrorism.