The original word terrorism comes from the french word terrorisme which was used to describe the policies of the Reign of Terror (1793-1794) during the French Revolution. Jacobin's invented this word to describe their own government policies. They only conceptualized it as what today is know as "state terrorism" however.
He word was then used by the British to describe the Irish Republicans under Wolfe Tone during their failed rebellion. This pejorative title for Irish Republicans stuck and would be use to refer to future republican organisations. As these organisations change tactics their actions would define what you today know as terrorism. This name would continue to derogatorily be used for Irish Republicans regardless of their tactics (uniformed open rebellion or peaceful protest). The Irish Fenians of the 1850's would likely be the first group that both their contemporaries and you would describe as a terrorist organisation.
As the 19th Century saw the rise of radicals and reactionaries ideas such as anarchism, fascism, and communism the word rapidly spread to include those who used tactics similar to the Fenians in Ireland.
The thing is, this is a derogatory term and very few groups that are rightly labeled terrorists would agree to such a title and many groups that are not terrorists by to day standards were labeled such at the time. (an example would be Charles de Gaulle who was labeled opponents by both the Nazis and Vichy French) Really only nihilist anarchists ever embraced the term.
The way we conceptualize terrorists today is largely through the lens of counter-terrorism. The first true anti-terrorism laws were the "Lois scélérates" (or villainous laws) restricting free speech in the third French Republic in the 1890's. These were largely detested among French republicans who saw them as unnecessary. The first truly popular efforts to counter terrorism came in the early 20th century to counter anarchists. It was actually after President McKinley's assassination by such an anarchist that America declared a "war on terrorism" for the first time
If this all seems very irresolute, it is. This is because the concept of terrorism and what is or isn't terrorism is far from a settled matter and much debated. Much of what was considered terrorism at the beginning might not be considered terrorism today and vis versa. What is and isn't terrorism has largely been a matter of politics and in the eye of the beholder.
This is not to say that what we call terrorism (civilian targeting by brutal underground political organisations) is a new phenomenon...far from it. These kinds of attacks are as old as civilisation. Assassination, murder, kidnapping, arson, for political gains were all favored by the Zealots of Judea 2000 years ago. I am only speaking of the conceptualizing of terrorism and being labeled as such.
Source:
What Terrorists Want Louise Richardson 2007
Terrorism in Context Martha Crenshaw 1995
Revolutionary Underground: The Story of the Irish Republican Brotherhood, 1858–1924 Leon O'Broin 1976