This rune is somewhat obscure in what it "actually" does, as the player does not need to actually "kill" enemies with Visc. Attacks. The way it functions is that when a Visc. Attack is triggered on the enemy, that enemy gets a temporary effect whereas, if it dies within the next few seconds (probably 4 seconds), then the Blood Echoes percentage increase is triggered.
The "Heir" symbol is quite strange, the two larger triangles with dots in it resemble the chalice that simbolized in the Communion rune (better depicted in the Hunter Chief Emblem), and then it has multiple interconnected line that almost resembles crosslines of lives that inevitable spread and yet converge. But then it is completely surrounded by dots, dots which usually mean blood in almost any other rune symbols. Putting it all together, it almost seems like a "sharing of blood", or a "family of blood", and the "heir" of that blood is the vessel who holds it.