I have heard this word used ad infinitum without truly understanding it.
1. From the Latin insurgēns. Rising upon or against. From insurgere. To rise up. From surgere. To rise.
2. Rebellious or in revolt. As against a government in power or the civil authorities.
3. A person who takes part in an uprising or rebellion. Insurrectionist.
4. In international law. A person or group that rises in revolt against an established government or authority but whose conduct does not amount to belligerency.
It is interesting to me that the insurgent does not amount to belligerency. That is. The insurgent is not engaged in a legally recognised war.