Jews refer to these same verses as "Shelosh-'Esreh Middot" (the Thirteen Attributes of God's Mercy). I've found that this passage is quoted/referenced many times in the Old Testament. Take a look at Numbers 14:17-18, Psalm 86:15, Psalm 103:8, Psalm 145:8, Joel 2:13, Jonah 4:2, Nahum 1:3, Nehemiah 9:17. Unfortunately, most of the times that I've read through this passage, I've found myself glossing over the words, uncertain of their exact meaning, but satisfied with a fuzzy understanding of them. But the other evening, as I was reading 1 Peter 1 in my head, I found myself pausing on the words "Blessed be the God and Father of our Lord Jesus Christ, who according to His abundant mercy..." And suddenly, I found myself wondering whether that was also a reference to Ex 34:6-7 and what the "abundant mercy" of God was like.
I did a couple word studies yesterday. I discovered that in Exodus 34:6, there are a few adjectives that are used to describe the LORD:
"merciful and gracious, longsuffering, abounding in goodness and truth"
The word רחום is translated "merciful". It appears in the Old Testament 13 times.
The word חנון is translated "gracious". It also appears in the Old Testament 13 times.
Interesting! Normally, these two words occur together - of the 13 occurrences, the words are paired 11 times. (They each occur independently here: "merciful/compassion" Dt 4:31, Ps 78:38 and "gracious" Ex 22:27, Ps 116:5).
It seems that "merciful" (רחום) refers to the kindness that God shows to those who are downtrodden. It expresses the compassionate love of God, as a heavenly Father, who cares for His children. The good Samaritan "showed mercy" and "had compassion" on the stranger who was injured (Luke 10).
It seems that "gracious" (חנון) refers to the kindness that God shows to those who are undeserving. While the man in John 9 said rightly that "God does not hear sinners," again and again in the OT we see that God hears the cries of His people and delivers them. He does it not because they deserve it, but because He is gracious (Ex 22:27). Paul says, "For by grace you have been saved...not of [your] works..." Ephesians 2:8-9
The word ארך is translated "longsuffering". It appears in the Old Testament 15 times. It expresses the patience of God in that He bears with mankind as He saves men and women and completes His plan of redemption. God could have ended the human race with Adam and Eve. Or God could have ended it at the Flood. Or He could have ended it yesterday - but instead, He is longsuffering. Peter says, "The Lord is not slack concerning His promise, as some count slackness, but is longsuffering toward us, not willing that any should perish but that all should come to repentance." 2 Peter 3:9
The word חסד is translated "lovingkindness" or "goodness". It appears in the Old Testament 248 times. Ex 34:6 says that God is abundant in lovingkindness. God says of Himself in Jeremiah 2:13 that He is "the fountain of living waters" and Jesus says in John 4 that "whoever drinks of the water that I shall give him will never thirst. But the water that I shall give him will become in him a fountain of water springing up into everlasting life." In 2 Cor 12, God tells Paul that "My grace is sufficient for you." David says in Psalm 23 that his cup "overflows"! Not only are the mercies of God good toward us, but they are "new every morning" (Lamentations 3:23). O, the deep, deep love of Jesus - vast, unmeasured, boundless, free!
The word אמת is translated "truth". It appears in the Old Testament 127 times. It refers to the absolute truthfulness of God, "who cannot lie" (Titus 1:2). If God sworn His mercy, grace, patience, and goodness to those who trust in Him, then He cannot fail on His oath. His trustworthiness is abundant. It is more abundant than all our fears, more abundant than all our faults, more abundant than anything we can give. He is the truth - and the way and the life (John 14:6).
These last two words (lovingkindness and truth) also appear together often in the OT.
How does the Lord Jesus show us what these mean? Here are some simple word searches from the gospel according to Matthew to give us all some food for thought and hopefully a starting place for further inquiry (1 Peter 1:10).
merciful and gracious
Matthew 9:36 - But when He saw the multitudes, He was moved with compassion for them...
Matthew 14:14 - And when Jesus went out He saw a great multitude; and He was moved with compassion for them...
Matthew 15:32 - Now Jesus called His disciples to Himself and said, "I have compassion on the multitude..."
Matthew 20:34 - So Jesus had compassion...
Matthew 9:13 - "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."
Matthew 12:7 - "But if you had known what this means, 'I desire mercy and not sacrifice,' you would not have condemned the guiltless."
Matthew 23:23 - "Woe to you, scribes and Pharisees, hypocrites! For you pay tithe of mint and anise and cummin, and have neglected the weightier matters of the law: justice and mercy and faith. These you ought to have done, without leaving the others undone."
Matthew 9:27 - "Son of David, have mercy on us!" (two blind men)
Matthew 15:22 - "Have mercy on me, O Lord, Son of David! My daughter is severely demon-possessed." (foreigner)
Matthew 17:15 - "Lord, have mercy on my son, for he is an epileptic..."
Matthew 20:30 - "Have mercy on us, O Lord, Son of David!" (two blind men)
Matthew 25:31-32 - "When the Son of Man comes in His glory, and all the holy angels with Him, then He will sit on the throne of His glory. All the nations will be gathered before Him, and He will separate them one from another, as a shepherd divides his sheep from the goats."
Matthew 17:17 - Then Jesus answered and said, "O faithless and perverse generation, how long shall I be with you? How long shall I bear with you?..."
Matthew 12:40 - "For as Jonah was three days and three nights in the belly of the great fish, so will the Son of Man be three days and three nights in the heart of the earth."
Matthew 22:16 - ..."Teacher, we know that You are true, and teach the way of God in truth..."
"Blessed be the God and Father of our Lord Jesus Christ, who according to His abundant mercy has begotten us again to a living hope through the resurrection of Jesus Christ from the dead..." 1 Peter 1:3
More information on Shelosh Esreh Middot: wikipedia and hebrew4christians (you have to go in alphabetical order down the list to "shelosh...")