Maximum HP increase with kerbals' level. A newbie has 100 HP while a 5-level kerbal has 150 (by default).
Kerbals' HP change, including in background and in timewarp, based on a range of factors such as living space, presence of crewmates, gravity, and specific ship parts. E.g., a level 1 kerbal will typically survive 11 days in a 1-man pod before becoming exhausted and turning into a Tourist.
Kerbals need time to restore their health at the KSC between flights.
If a kerbal's health goes under 20%, he/she is exhausted and becomes a tourist. They will go back to work when health grows back to 25%.
If a kerbal's health falls to 0, he/she dies!
Kerbals experience radiation, both cosmic and artificial, which permanently affects their maximum health.
You can protect from radiation by using shielding and choosing safer mission profiles.