Genesis 22
1 And it came to pass after these things, that God did tempt Abraham, and said unto him, Abraham: and he said, Behold, here I am.
2 And he said, Take now thy son, thine only son Isaac, whom thou lovest, and get thee into the land of Moriah; and offer him there for a burnt offering upon one of the mountains which I will tell thee of.
And thus we learn that a good Christian is one who is willing to sacrifice all for the glory of God :)
The belief in a God and a corresponding afterlife is not the be all and end all, of course. The key is a belief that you are the good guys. Truly obscene crimes like this our only ever built on the best of human qualities. Love, selflessness, honour etc etc. The bad guys don't have it in them.
So a parent will need to love their child. To want what's best for them. And what can be better than a life of meaning, a life in service to god and your fellow man, a life rewarded by paradise in the next?
If the alternative life is a grim fight for survival without hope of improvement, then the argument in favour of suicide bombing is all the stronger. Add to that a cheapness of life that is grown from seeing so many others die from war and disease. Dehumanise the enemy so it no longer feels like a crime but a heroic strike against evil. Then add a financial reward for the surviving family because, at the end of the day, eating is important.
Is it that hard to imagine why the parents do it?