Threat Axis is the main direction of where the enemy is coming from. The key to winning battles is to focus and contain the threat axis as much as possible, meaning your troops have free mobility to move into flanking positions.
The Threat Axis when you first start is the Deployment Area where the opposing player will be coming from. Blue would have the Threat Axis from the East, or right side, with Green from the West, or left side. Typically the challenged player has the Green deployment zone.
As turns progress the Threat Axis may be in front of you, behind you, or to the sides of your positions. This is why small units have success where individuals will not. Fire Teams will be able to cover each other's blind zones, putting more fire towards the enemy and scouting, and when you use a military strategy broken down into Elements, you will be able to keep that Threat Axis contained.
It is possible to be stuck in a position with multiple Threat Axis bearings around you - this is called being trapped or pinned down where your movement is severely restricted. Staying in this position for more than a turn without being wiped out is rare indeed.
Note: If you are in danger of being pinned down, one tactic to take is to try and break down a wall to escape unnoticed. See Wallbusting for more information on this.