It only affects targeted operations, used against armies, cities, and sectors.
if you zoom out and switch to the operations view you can see individual operations defense for each sector. The Syndicate skill, and any operations that affect a sectors operations defense, reduce this sector based defense. When you have a targeted operation selected and ready to launch, it will show your %chance of success when you mouse over a target, which scales with your operations offense versus the sectors operations defense. Note that Alert Level affects the entire operations defense of a faction, not just their covert (global) defense.