Health is the measure of how fit a unit is, as a unit receives damage it's health is decreased until it reaches zero and it dies.
A unit's health is displayed as a colored bar next to the unit (the bar appears when a unit is selected). When a unit is in full health the bar is a solid green. As a unit starts taking damage the bar starts turning translucent to yellow then to red. When a unit's health is red it is on death's door - it can still move and fight at full effectiveness but it's luck has run out and another attack or two (a sword hit or arrow) will kill the unit.
A unit's health can be effected by healing spells or sometimes other magical artifacts.