In Shakespeare's Macbeth, my understanding of this quote has always been that "blood begets blood," or that if blood is shed, it means more bloodshed will follow.
In Act III, scene four (a great scene for those who like the supernatural), Banquo's ghost has visited Macbeth several times. The Elizabethans believed that if a person had met with a violent end, he might walk the earth. Macbeth is having a banquet and keeps saying he wishes Banquo were there, and so Banquo shows up, but no one else can see him.
"...the time has been. / That when the brains were out, the man would die." (III.iv.79-80)
This is almost a comical line: it used to be that when you killed a man, he stayed dead. His remarks, in that he alone sees Banquo, sound ridiculous.
Macbeth has been a little unbalanced since he murdered Duncan—of which Lady Macbeth reminds him—so his reaction to ghosts, most especially something he cannot fight, pushes him to his wits' ends. He admits:
What man dare, I dare: / Approach like the rugged Russian bear, / The armed rhinoceros, or the'Hyrcan [wild] Tiger, / Take any shape but that, and my firm nerves / Shall never tremble... (III.iv.101-105)
I can fight the most frightening of animals that any man could face (bears, tigers, the rhinoceros), but I cannot face ghosts.
Macbeth's comment "blood will have blood," is followed by a list of unnatural occurrences that began to take place the night he murdered Duncan. The Elizabethans also believed it a mortal sin to kill a king because God ordained (decided) who would be king. With Duncan's death, there is a disruption to the universe: the wrong man sits on the throne. And until that changes, earthquakes and eclipses will occur; and gravestones will move and trees will speak.
Stones have been known to move and trees to speak. (III.iv.125)
So Macbeth believes there is more bloodshed to follow: bloodshed breeds bloodshed. However, his closing comment for the act promises that he will be personally responsible for some of this bloodshed:
...My strange and self-abuse / Is the initiate fear that wants hard use; / We are yet but young in deed. (III.iv.14-16)
In other words, the visions he has seen are simply due to a lack of experience with murder: with more experience, he'll feel better; and, after all, they've only just begun.