Hit Points are usually described as an abstract fighting or health force within a character or creature that lets them keep going until it reaches zero. Of course, in an actual game this is sufficient. There are also some people like myself who prefer to describe “hit points as meat points”, aka all hit points are physical damage and the amount of physical damage you can take increases with level. Because higher level or tougher character can survive unrealistic amounts of damage, this opens the door to the concept of the hows and whys, in universe, “hit points as meat points” work.
 They're made of stronger stuff. Their skin is tough as leather, their muscle and flesh is like cutting into wood. Your sword can bite their skin, but only goes in a few inches even with all your might. Their blood may also be thicker then normal, clotting up wounds quickly. This could go up to include automatic beneficial mutations such as your bones being remade out of metals, or your skin taking on a golden hue to represent a more metallic consistency of flesh.
 They surround themselves in an invisible energetic field. This isn't necessarily a martial art or magical spell, it may just be an innate property of things that get powerful. This energy deflects weapons and make their points flow or bounce off their skin, but it isn't the same as having standby armor or deflection as each time this field absorbs or weakens a blow, it uses up some of its energy. Hence, it works as a reserve of hit points.
 The setting is described not using real life terms, as such real life physics don't apply. Things only die when at least one of their four elements (breath for air, body heat for fire, etc.) are expelled to the cosmos. It is entirely possibly a high level warrior has so much wind in their breast that stabbing through both lungs won't kill them alone. Perhaps their humors are too well circulated, or their warrior spirit burns too hot and you can only defeat them by wearing it away.
 Spiritual authority means that blades and crushing forces simply harm them less. Their skin is no stronger then anyone else, their blood is no thicker then anyone else, weapons just don't hurt them as much. You slam their head with your hammer and the skull doesn't crack, even though the force you put into the blow would. Your arrow simply pierces a tiny pinhole, not because their skin is harder then stone but because it refuses to harm one of spiritual superiority. Once injuries mount however, then weapons begin to deal more damage to their form, reducing their invincibility. It could be then that “real” wounds begin once hit points reach zero, as though this godly protection of Numen wore off once their fatigue sets in.
 Characters simply have an unnatural hold on life. You can hurt them the same as any real creature, but it doesn't stop them up to a certain threshold. You can pierce their heart, shatter their skull, cut the tendons in their arms and they can still move and think and fight until enough damage is dealt. Could imply that the undead are just people with a super powerful will to live, continuing after death.
 High powered warriors regenerate from fatal or near-fatal damage very quickly, as though their reserve of life force prevents a final blow, though shallower cuts take a nearly normal amount of time to heal. This means any killing blow is healed over quickly, but they can still accumulate damage and eventually die if enough is dealt. If characters heal at different speeds based on hit points, such as a percentage or class based amount, then it is a little more fitting in universe.