Combat Intuition allows you to sense if an unseen enemy is aiming at you. You will only get the warning if the enemy is NOT on your Radar, and if their crosshairs are directly on you.
Under normal circumstances, enemy combatants do not appear in the player's on-screen radar unless they fire a shot or sprint within a certain radius of the player. Combat Intuition can be used as an effective counter to this, and provide some warning of a sneak attack.
With Combat Intuition selected, an enemy taking aim at the player will be exposed on the radar map. Additionally, a yellow marker will appear on screen to alert the player of the enemy combatant and what direction they're aiming from.
To avoid triggering Combat Intuition on a target, a player can make sure to appear on the enemy radar before taking aim, for example by firing a shot from a non-silenced weapon or sprinting within hearing range (provided Silent Running haven't been chosen).
An operative using Comms Hack will effectively disable Combat Intuition for his entire team for the duration, as it causes all enemies to appear on radar.