Third party insurance is the legal minimum in all EU countries (and most other European countries). It covers you against any injury or damage to anyone else (other road users including pedestrians, other cars including their occupants, damage to buildings ....). This is nothing to do with hire cars, it applies to all motor vehicles.
As this is a legal requirement, without which you cannot legally drive a car on a public road, it is a given, which is why you cannot find a reference to it as an extra for car rentals.
By EU law, all vehicles must have 3rd party insurance valid in all EU countries.
But, that does not cover damage you do to yourself or to the hire car. If you do any damage to a hire car, anything from a paint scratch to a complete write-off, the car hire company is going to come after you for the cost of repairing their car. You avoid this by add-on insurance called "Collision Damage Waiver". This CDW can often be more than the actual rental cost. You don't have to have CDW, but if you don't and you damage the car, it can get very expensive.
This is the same as if you owned a car. You must legally have 3rd party insurance, but "fully comprehensive" insurance to cover damage to your own car is optional.
CDW will not cover injury to yourself. If you are not an EU/EEA resident you need medical cover, including worst-case medical repatriation.
Re Edgar's post: I am somewhat dubious as to whether a car hire company in Norway or France would accept a policy from a foreign insurance company in a foreign language as covering the local legal requirement for 3rd party cover. They already have a blanket policy. I think the link you posted is more approprite to 3rd world countries without legal minimum insurance requirements.