Albert Barnes Commentary Psalms 51:17

"The sacrifices of God are a broken spirit: A broken and contrite heart, O God, thou wilt not despise." — Psalms 51:17 (ASV)

The sacrifices of God - The sacrifices which God desires and approves; the sacrifices without which no other offering would be acceptable. David felt that what he specified here was what was demanded in his case.

He had grievously sinned; and the blood of animals offered in sacrifice could not put away his sin, nor could anything remove it unless the heart itself were penitent and contrite.

The same thing is true now. Though a most perfect sacrifice, in every way acceptable to God, has been made for human guilt by the Redeemer, it is still as true now as it was under the old dispensation concerning the sacrifices then required, that even that sacrifice will not avail for us unless we are truly penitent; unless we come before God with a contrite and humble heart.

Are a broken spirit - A mind broken or crushed under the weight of conscious guilt. The idea is that of a burden laid on the Soul until it is crushed and subdued.

A broken and a contrite heart - The word rendered "contrite" means to be broken or crushed, as when the bones are broken (Psalms 44:19; Psalms 51:8); and then it is applied to the mind or heart as that which is crushed or broken by the weight of guilt. The word does not differ materially from the term “broken.” The two together constitute intensity of expression.

Thou wilt not despise - This means You will not treat such a heart with contempt or disregard. That is, God would look upon such a heart with favor, and to such a heart he would grant his blessing. See the notes at Isaiah 57:15 and Isaiah 66:2.