Asking for the right things
This was the crowd's response to Pilate when he turned Jesus over to them, refusing to endorse His crucifixion. Pilate found nothing about Jesus that violated Roman law. Further, his conscience told him that what was happening was wrong, and that he should take no part in it.
The crowd had been worked up into such a frenzy, though, that they would not take "no" for an answer. When Pilate said he would not be responsible for Jesus' execution, the crowd responded with misguided bravado, as if to say, "Fine, we will take responsibility for this."
But the wording in the verse is very noteworthy. "Let His blood be on us and our children" was the crowd's way of accepting the responsibility. But in fact, what they were asking for is precisely what they needed most of all. Jesus died as the ultimate, perfect sacrifice and atonement for our sins. The animal sacrifice system was put in place to offer death and blood as payment for sin. As the Lamb of God, Christ's death was the ultimate sacrifice, and His blood covers us once and for all.
"Let His blood be on us and our children" is exactly what we should be asking for today. We are responsible for His death, because our sin created the situation whereby His death was necessary. But His death, and our covering in His blood as atonement for our sin, is the greatest blessing we could ever receive.
Sometimes we are asking for the right things, even when we have no idea what or why we are asking.