Extrastate wars are between a state or country and a group that doesnt we call a non-state actor, this is a group that excists somewhere else in the world.
A great example of a non-state actor is a terrorist organisation. They are not a country so it is not interstate, and they are not in the same country so it is not intrastate.
Terrorist organisations are groups of people who work together to achieve their goal through terrorism.
Terrorism are all forms of violence that can be used to make people afraid.
Important to note is that terrorist organisations and terrorism can be an example of extrastate wars. However that does not mean that acts of terrorism are always part of an extrastate war.
This is only the case when its about lenghty conflicts. So conflicts that take a long time.
Now you must wonder what acts of terrorism are when they are not part of an extrastate war. If these terrorists are not part of an organisation we call them 'Lone Wolves'. They act alone and these attacks can be quite random.
The most well known examples of terrorist organisations are Al Qaeda and IS. And the most well known act of terrorism would be '9/11' which refers to a series of attacks in the United states.
An example of a Lone wof is Anders Breivik who staged attacks in Norway in 2011 which consisted of bombings and a shooting. Anders reasoning for his actions was that he disagreed with his government.