In The Crucible, what does Hale mean when he says, "There is blood on my head"?
Mr. Hale says that there is blood on his head because he feels responsible for the deaths of the innocents who have been hanged prior to Act Four as well as for those folks scheduled to hang in the final act of the play. He had concerns early in the play, as early as his conversation with the Proctors, in Act Two, on the night Elizabeth Proctor was arrested. When he learns that Rebecca Nurse had been accused, he is "deeply troubled," and he tells her husband, Francis,
[I]f Rebecca Nurse be tainted, then nothing's left to stop the whole green world from burning. Let you rest upon the justice of the court; the court will send her home, I know it.
And yet, Rebecca is not sent home; she is convicted of witchcraft and sentenced to die. Hale sits and waits for weeks, though he has reservations about the court and its proceedings, and, when he finally does speak up (in Act Three), he becomes so angry when Danforth dismisses him that he simply leaves Salem altogether. He shouts, "I denounce these proceedings, I quit this court!" and he leaves.
Hale doesn't stay and try to combat the court's obvious corruption, despite his knowledge that these convicted are innocent. Therefore, he does too little too late, and he fails to stand up for the innocent when it could have made a difference. In this sense, then, Hale was too complacent, too afraid to rock the boat when it could have mattered, and he feels all the weight of that responsibility in Act Four when he talks about the blood on his head.
This quote is said by Reverend Hale in Act IV, when it is clear that the witch hunt has moved on somewhat, and a number of people have now been hung for their supposed "crimes." Hale, instead of being the first instigator of the witch hunt, who zealously questioned Tituba in Act I, is now a broken man who denounces the whole proceedings, as his swift exit from the court at the end of Act III demonstrates. Now, he spends his time working with those due to be hung, trying to encourage them to lie and confess to crimes they didn't commit to spare their lives. Note how he describes his new work:
I come to do the Devil's work. I come to counsel Christians that they should belie themselves. There is blood on my head! Can you not see the blood on my head!
It is clear from these words that Hale feels, at least in part, responsible for the deaths of those who went to the gallows refusing to confess to crimes they didn't commit. He, unlike Danforth, is able to see the massive mistake that has been made and how the court has been accusing and sentencing to death innocent people. Because he was involved in that process, at least initially, he feels himself to be culpable. It is clear from the quote that this is something that haunts and disturbs him deeply.