What is the meaning of the term “I desire mercy and not sacrifice”, spoken by Jesus.

Matthew 9:9-13 (NKJV)
9 As Jesus passed on from there, He saw a man named Matthew sitting at the tax office. And He said to him, “Follow Me.” So he arose and followed Him.
10 Now it happened, as Jesus sat at the table in the [Matthew’s] house, that behold, many tax collectors and sinners came and sat down with Him and His disciples.
11 And when the Pharisees saw it, they said to His disciples, “Why does your Teacher eat with tax collectors and sinners?”
12 When Jesus heard that, He said to them, “Those who are well have no need of a physician, but those who are sick.
13 But go and learn what this means: ‘I desire mercy and not sacrifice.’ For I did not come to call the righteous, but sinners, to repentance.”

Who did Jesus “call”? Matthew, a sinner who was sick, who repented. Why? He had need of a physician.

Mark 2:17 (NKJV)
17 When Jesus heard it, He said to them, “Those who are well have no need of a physician, but those who are sick. I did not come to call the righteous, but sinners, to repentance.”

Mark 3:1-6 (NKJV)
1 And He entered the synagogue again, and a man was there who had a withered[G3583] hand.
2 So they watched[G3906] Him closely, whether He would heal him on the Sabbath, so that they might accuse Him.
3 And He said to the man who had the withered hand, “Step forward.”
4 Then He said to them, “Is it lawful on the Sabbath to do good or to do evil, to save life or to kill?” But they kept silent.
5 And when He had looked around at them with anger, being grieved by the hardness of their hearts, He said to the man, “Stretch out your hand.” And he stretched it out, and his hand was restored as whole as the other.
6 Then the Pharisees went out and immediately plotted with the Herodians against Him, how they might destroy Him.

Jesus saved this man’s life, both physically and spiritually. This was a good thing. Evil would have been to not heal him, ending in his death.

Matthew 12:1-14 (NKJV)
1 At that time Jesus went through the grain fields on the Sabbath. And His disciples were hungry, and began to pluck heads of grain and to eat.
2 And when the Pharisees saw it, they said to Him, “Look, Your disciples are doing what is not lawful to do on the Sabbath!”
3 But He said to them, “Have you not read what David did when he was hungry, he and those who were with him:
4 how he entered the house of God and ate the showbread which was not lawful for him to eat, nor for those who were with him, but only for the priests?
5 Or have you not read in the law that on the Sabbath the priests in the temple profane the Sabbath, and are blameless?
6 Yet I say to you that in this place there is One greater than the temple.
7 But if you had known what this means, ‘I desire mercy and not sacrifice,’ you would not have condemned the guiltless.
8 For the Son of Man is Lord even of the Sabbath.”
9 Now when He had departed from there, He went into their synagogue.
10 And behold, there was a man who had a withered hand. And they asked Him, saying, “Is it lawful to heal on the Sabbath?”–that they might accuse Him.
11 Then He said to them, “What man is there among you who has one sheep, and if it falls into a pit on the Sabbath, will not lay hold of it and lift it out?
12 Of how much more value then is a man than a sheep? Therefore it is lawful to do good on the Sabbath.”
13 Then He said to the man, “Stretch out your hand.” And he stretched it out, and it was restored as whole as the other.
14 Then the Pharisees went out and plotted against Him, how they might destroy Him.

The Pharisees would have sacrificed Jesus’ disciples even though they were guiltless. They would have rather let people die than be healed too. This is an evil they had put on people, God hadn’t. They thought it was righteous for the priests to kill the sacrificial lambs on the Sabbath. Jesus says: having mercy is better than sacrificing. Later Jesus himself would do just that and have mercy on us by sacrificing Himself. He considered the act of sacrificing His life to be “mercy” and did not think it a “sacrifice”.

Luke 5:29-32 (NKJV)
29 Then Levi gave Him a great feast in his own house. And there were a great number of tax collectors and others who sat down with them.
30 And their scribes and the Pharisees complained against His disciples, saying, “Why do You eat and drink with tax collectors and sinners?”
31 Jesus answered and said to them, “Those who are well have no need of a physician, but those who are sick.
32 I have not come to call the righteous, but sinners, to repentance.”

Luke 6:6-11 (NKJV)
6 Now it happened on another Sabbath, also, that He entered the synagogue and taught. And a man was there whose right hand was withered.
7 So the scribes and Pharisees watched Him closely, whether He would heal on the Sabbath, that they might find an accusation against Him.
8 But He knew their thoughts, and said to the man who had the withered hand, “Arise and stand here.” And he arose and stood.
9 Then Jesus said to them, “I will ask you one thing: Is it lawful on the Sabbath to do good or to do evil, to save life or to destroy?”
10 And when He had looked around at them all, He said to the man, “Stretch out your hand.” And he did so, and his hand was restored as whole as the other.
11 But they were filled with rage, and discussed with one another what they might do to Jesus.

This is an interesting thing; the Scribes and Pharisees thought Jesus could heal the man. They wanted Jesus to do it too, but not for the reason of doing good but so they could accuse Him of doing wrong. If you were to witness a miracle, would you think evil of it or good? They were so blinded by their evil hardened hearts, they could only think evil and wrongly. This is twisted.

Hosea 6:4-7 (NKJV)
4 “O Ephraim, what shall I do to you? O Judah, what shall I do to you? For your faithfulness is like a morning cloud, And like the early dew it goes away.
5 Therefore I have hewn them by the prophets, I have slain them by the words of My mouth; And your judgments are like light that goes forth.
6 For I desire mercy[H2617] and not sacrifice, And the knowledge of God more than burnt offerings.
7 “But like men they transgressed the covenant; There they dealt treacherously with Me.

Jesus had quoted Himself from the Old Testament. To know God would make you merciful. If they were righteous they would not need to sacrifice for the forgiveness of their sins. God had chastened His people Israel many times but they would not change their ways, therefore He would have to sacrifice Jesus for their sins but He considered it mercy. He did the same for you and me. He would have us be like Him. Do not consider your goodness and kindness to others a sacrifice but love. His love is greater than all else.

Stg H2617 Translated “mercy” in Hosea 6:6
hesed – A masculine noun indicating kindness, lovingkindness, mercy, goodness, faithfulness, love, acts of kindness.
The Complete Word Study Dictionary – Old Testament.

Stg: G3583 Translated “withered” in NKJV Mt 12:10, Mk 3:1, Lk 6:6
xēraínō; fut. xēranó, aor. exérana (James 1:11), perf. pass. exérammai (Mark 3:1), 3d person sing. exérantai (Mark 11:21), from xērós <G3584>, dry. To dry or make dry. Of plants, to dry up, wither (James 1:11). In the pass.: to be dried up, become dry, wither away (Matt. 13:6; 21:19, 20; Mark 4:6; 11:20, 21; Luke 8:6; John 15:6; 1 Pet. 1:24); of fluids, to be dried up (Mark 5:29; Rev. 16:12; Sept.: Gen. 8:7; 1 Kings 17:7; Isa. 19:5); of the body or its members, to wither, pine away (Mark 3:1, 3; 9:18;
The Complete Word Study Dictionary – New Testament.

Stg: G3906 Translated “watched” in NKJV
paratēréō; contracted paratēró, fut. paratērésō, from pará <G3844>, near or close, to and tēréō <G5083>, to keep, observe. To watch closely, observe, as the gates of a city (Acts 9:24; Sept.: Ps. 37:12); to observe a person insidiously (Mark 3:2; Luke 6:7; 14:1; 20:20)
The Complete Word Study Dictionary – New Testament.

The Word also says:

1 Samuel 15:22 (NKJV)
22 So 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 heed than the fat of rams.

God seeks our obedience to Him so that we do not make it a sacrifice. If we love Him we will want to obey Him and we will not consider it a sacrifice to do so. If we want life to be abundant we will obey Him. He did not consider His death on the cross to be a sacrifice because He had mercy on us. He wanted us to have life, His life, and that more abundantly. Do good and bring life to others as He did for us. Jesus said He came to preach the gospel to the poor, to heal the brokenhearted, proclaim liberty to the captives, recovery of sight to the blind, set at liberty those who are oppressed, proclaim the acceptable year of the LORD, feed the hungry, clothe the naked, care for the orphans. We should do likewise because of love. His love becomes our love when we give it. When we give it, we have it. It is active.