Why do people offer sacrifices?

In their dealing with God, people offer prayers and sacrifices. Sacrifices serve several purposes. To thank the deity for the favour granted. To appease the deity. To repay the wrongs done. To die in my stead. To join the partakers into one etc. We should be grateful to God for all His blessings. In return, we show our gratitude by offering sacrifices. When disasters strike, we prevent further damages by offering sacrifices to pacify the wrath of God. When we have done wrong, we repay with sacrifices. When the wrong is so grave that we should die, we kill a bull in our stead. In ceremonies, offering sacrifices join the partakers into one community etc.
Now, the author of Hebrews focuses on one aspect of sacrifices to show that Jesus' sacrifice excels the previous sacrifices under the Old Covenant. The previous tent was only a shadowy copy. The previous sacrifices fail to make perfect those who offer them.
For since the law has but a shadow of the good things to come instead of the true form of these realities, it can never, by the same sacrifices which are continually offered year after year, make perfect those who draw near (Hebrews 10:1).
These previous sacrifices were inferior because the blood of bulls and goats failed to take away sins. Only the blood of Christ can.
But in these sacrifices there is a reminder of sin year after year.
For it is impossible that the blood of bulls and goats should take away sins (Hebrews 10:3-4).

Christians are blessed because they have been redeemed with the precious blood of Christ. In fact, God is not blood-thirsty. He does not desire blood nor fat of the animals. He wants us to do His will. God wants us to love Him and our neighbours.

Dear Lord, You have ransomed us with a high price. Now, it is our turn to make good use of this freedom to build the kingdom of God on earth. Amen.

Appendix:
Sacrifices and offerings thou hast not desired, but a body hast thou prepared for me;
in burnt offerings and sin offerings thou hast taken no pleasure.
Then I said, `Lo, I have come to do thy will, O God,' as it is written of me in the roll of the book."θυσίαν καὶ προσφορὰν οὐκ ἠθέλησας, σῶμα δὲ κατηρτίσω μοι·
ὁλοκαυτώματα καὶ περὶ ἁμαρτίας οὐκ εὐδόκησας.
τότε εἶπον· ἰδοὺ ἥκω, ἐν κεφαλίδι βιβλίου γέγραπται περὶ ἐμοῦ, τοῦ ποιῆσαι ὁ θεὸς τὸ θέλημά σου. (Hebrews 10:5b-7)
θυσίαν καὶ προσφορὰν οὐκ ἠθέλησας, ὠτία δὲ κατηρτίσω μοι, ὁλοκαύτωμα καὶ περὶ ἁμαρτίας οὐκ ᾔτησας.
τότε εἶπον Ἰδοὺ ἥκω, ἐν κεφαλίδι βιβλίου γέγραπται περὶ ἐμοῦ,
τοῦ ποιῆσαι τὸ θέλημά σου, ὁ θεός μου (Psalm 39:7-9a LXX, 40:7-9a MT)

Thou hast neither desired nor taken pleasure in sacrifices and offerings and burnt offerings and sin offerings
θυσίας καὶ προσφορὰς καὶ ὁλοκαυτώματα καὶ περὶ ἁμαρτίαςοὐκ ἠθέλησας οὐδὲ εὐδόκησας, (Hebrews 10:8)
And Samuel said, "Has the LORD as great delight in burnt offerings and sacrifices, as in obeying the voice of the LORD? Behold, to obey is better than sacrifice, and to hearken than the fat of rams.
καὶ εἶπεν Σαμουηλ Εἰ θελητὸν τῷ κυρίῳ ὁλοκαυτώματα καὶ θυσίαι ὡς τὸ ἀκοῦσαι φωνῆς κυρίου; ἰδοὺ ἀκοὴ ὑπὲρ θυσίαν ἀγαθὴ καὶ ἡ ἐπακρόασις ὑπὲρ στέαρ κριῶν, (1 Samuel 15:22).

Lo, I have come to do thy will.ἰδοὺ ἥκω τοῦ ποιῆσαι τὸ θέλημά σου (Hebrews 10:9b)
I delight to do thy will, O my God; thy law is within my heart.τοῦ ποιῆσαι τὸ θέλημά σου, ὁ θεός μου, ἐβουλήθην καὶ τὸν νόμον σου ἐν μέσῳ τῆς κοιλίας μου. (Psalm 39:9 LXX, 40:9 MT)