The psalmist continues praising the LORD’s goodness, and now he speaks of what is the proper response to the LORD’s great mercy; it is not sacrifices but obedience.
Four words are used for sacrifices in verse 6: Sacrifice (zevich) is the regular word for animal sacrifices in general; sometimes it designates a fellowship offering, in which only a part of the animal was burned on the altar; some of it was given to the priest and the rest was eaten by the worshipers. Offering (minchah) originally was used of both animal and grain offerings, but later was restricted to grain offerings (which is probably what it means here). Burnt offering (ʿolah) was the sacrifice of an animal that was completely burned on the altar. Sin offering (chataʾah) was an offering made in order to have sins forgiven. The list is not complete; there were other sacrifices. The important thing here is that the psalmist, by using these four as representative, is placing sacrifices in their proper perspective (see similar statements in 1 Sam 15.22; Psa 50.8-14; 69.30-31; Amos 5.21-22; Micah 6.6-8); above all, God wants the total and complete obedience of those who worship him, and not just the sacrifices they offer to him.
In some languages it will be difficult to make distinctions between the various kinds of sacrifice, particularly in languages where the term “sacrifice” is translated as “burned gifts offered to God.” In such languages one may have to use the term for sacrifice three times, but accompanied by the qualifications provided in lines b and c; for example, “you do not want burned gifts offered to you, and other gifts; you do not ask for animals to be burned in order to take away people’s sins.”
The psalmist says thou dost not desire and thou hast not required, but it is probable that these statements are not meant literally; this is rather an emphatic way of saying “Sacrifices are not the only thing you want.” It is recommended, however, that the translation faithfully represent the meaning of these two absolute statements: God does not want, nor does he require, that his people offer him sacrifices.
As the Revised Standard Version order of lines shows, line b in Hebrew (literally “you have dug ears for me”) has been placed in Good News Translation at the end of the verse, to connect logically with the beginning of verse 7. The meaning is that God gave the psalmist the ability to hear the LORD’s command and to obey it (see Isa 50.5). One translation may be “you taught me the meaning of obedience”; New American Bible “ears open to obedience you gave me.” Bible en français courant, however, translates “you have made me understand that very well” (referring to the preceding statement) and New Jerusalem Bible is similar; this does not seem very likely.
The Hebrew order of statements as reflected in Revised Standard Version is negative–positive–negative. Good News Translation shifts this order to become negative–negative–positive. In languages where it is poor style to have the parallelism interrupted by but thou hast given me an open ear, it may be clearer in the receptor language to keep them together, as Good News Translation has done.
Quoted with permission from Bratcher, Robert G. and Reyburn, William D. A Handbook on the Book of Psalms. (UBS Helps for Translators). New York: UBS, 1991. For this and other handbooks for translators see here .

Thanks
Piercing ears is also a reference to Ex 21:6 meaning having decided to become permanently slave to a master (here God).