Health, is a measure of a soldier's physical condition. Health is shown as a red guage in the Bio pane. If you have no armor, all damage taken will come from your health, but with armor only a fraction of the damage will come from your health. Pain Fields, the Radiator, and the Damage Crystal bypass your armor and affect your health directly.
The Health Module can also recover your health. When you are within the SOI of a base with this benefit, you health will slowly regenerate. The Health Module also raises your maximum health to 120/120.
The Health of friendly soldiers can be seen above their heads as a green bar, if close enough, with black sections indicating damage. The Health of enemy soldiers can be seen with the Enhanced Targeting Implant, as a red bar.