Health Regeneration is a stat that is becomes increasingly effective the more Health your Champion has. As such, it is widely invested by players who use Tanks, most notably Warriors who also have innate skills that boost Health Regeneration such as Rally Cry and Final Charge. However, Mages or Rouges that are heavily invested in Health or Constitution can also make use of this stat.
It regenerates a certain percentage of Health every game tick, which is approximately one second. Due to this, it can be used to negate the DoT of Bleed, which has a similar effect.
The formula to calculate the value of Health Regeneration is as follows:
Health Regeneration = (Total health)*(Regeneration Bonus %) * (0.5)
A scenario would be:
A Champion with 1000 Health and a 10% Regeneration Bonus (converted 0.1 in decimal form)
Health Regeneration = (Total health)*(Regeneration Bonus %) * (0.5)
= (1000 Health)*(0.1 Regeneration Bonus) * (0.5)
= 50 Health/Tick
If the answer is a decimal, then round to the nearest whole number.
Note that while the value of Health Regeneration is also visible by hovering over Health in the Party Screen, this value is off by a few points due to the negligence of rounding.
Here is a calculator for the lazy people: