Maybe it's because I'm too young to know this but... What was exactly "Operation Gladio" and what were the "stay-behind" units ?

First off, there was never an "Operation" Gladio. Gladio is the name of one of the various NATO stay behind armies, which, de jure, were only supposed to protect Western Europe in case of Soviet invasion. The Gladio army operated in Italy.

These armies have been accused of terrorist activities by various persons and organizations, including swiss historian Daniele Ganser (University of Basel) writer of the book "NATO's Secret Armies: Operation Gladio and Terrorism in Western Europe". Ganser used the document "U.S. Army Field Manual 30-31B" as a source that these armies were involved in terrorist activities. This document states that a strategy of tension must be used, involving violent attacks which are then blamed on left-wing groups in order to convince governments of the need for counter-action. However, the US State Department claims the document was forged by the soviets.

Ray S. Cline, a former CIA official told the BBC in the second of a three part documentary on Gladio, that the document was authentic, and that the CIA gave it to him.

To this day, there isn't a consensus on how these armies actually worked, and their responsability in various terrorist attacks.

There has been however, multiple investigations conducted by European countries and institutions .In 1990 the European Parliament reached polemic conclusions about those armies and their involvement in terrorism. The full document can be read by clicking the former link.

Here is a transcipt of the most relavant parts:

RESOLUTION

on the Gladio affair

The European Parliament.

A. having regard to the revelation by several European governments of the existence for 40 years of a clandestine intelligence and armed operations organization in several Member States of the Community,

B. whereas for over 40 years this organization has eluded all democratic controls and has been run by the secret services of the states concerned in collaboration with NATO.

C. fearing the danger that such clandestine networks may have interfered illegally in the internal political affairs of Member States or may still do so.

D. whereas in certain Member States military secret services (or uncontrolled branches thereof) were involved in serious cases of terrorism and crime as evidenced by various judicial inquiries.

...

2. Protests vigorously at the assumption by certain US military personnel at SHAPE and in NATO of the right to encourage the establishment in Europe of a clandestine intelligence and operation network;

Calls on the governments of the Member States to dismantle all clandestine military and paramilitary networks; "

According to this report, these armies were indeed involved in some way in terrorism. No further investigations by the european parliament have been done since.

The report is also available in many other european languages.