The sacrifices of God are a broken spirit; a broken and contrite heart, O God, you will not despise.” (Psalm 51:17, ESV)

We do not normally think that anything broken is good, a broken tool is useless, a broken appliance can no longer help us, a broken relationship is one that is severed and no longer a source of joy and comfort and friendship.

Not everything broken is useless, however; here God delights in broken hearts.  Broken hearts are sacrifices that say, “I cannot do life on my own, I am dependent upon you.”  This attitude God will not despise [to regard something as contemptible or worthless].

Spurgeon: “Never yet has God spurned a lowly, weeping penitent, and never will he while God is love, and while Jesus is called the man who receiveth sinners.”

“Though God loves a whole heart in affection, yet he loves a broken heart in sacrifice.” – Sir Richard Baker

Just so.