This mechanic arrived with the La Résistance DLC — without it you won't have access to the intelligence agency. With it active, your ability to spy (or be spied on) becomes a game within the game.
Espionage Operations
You recruit and train agents, and infiltrate them into a target country. Once inside, you can launch specific operations: steal tech blueprints, sabotage their industrial production, damage their army or navy, or even lay the groundwork for a coup. Each operation consumes time and resources from your agency, so you need to prioritize instead of trying everything at once.
Code-Breaking
If you dedicate enough resources to it, you can start decrypting another country's radio communications, giving you partial visibility into their military movements and how they're fighting the war. It's one of the quietest but most valuable advantages of the mechanic: knowing where the enemy is going to strike is worth more than almost any one-off sabotage.
Counter-Intelligence
Just as you can spy, other countries can infiltrate agents into yours. Counter-intelligence detects and neutralizes those enemy operations before they do damage. Ignoring it entirely leaves your industry and army exposed to sabotage you won't even know the source of.
Common Mistakes
The most common mistake is treating the intelligence agency as an optional luxury and not assigning it budget or staff, leaving it inactive the whole game. The second is concentrating all your espionage capacity on a single target country when the threat (or the opportunity) is actually coming from several fronts at once.