These three parables are three aspects of the Kingdom of heaven:
The Treasure
As in the parables of the Sower, and the Wheat and the Tares, the man here is the Lord Jesus.
Israel, the people that God Himself had originated in antiquity to be His testimony on earth, lost its territorial heritage because of its infidelity to God, and was spread throughout all the earth.
God, however, knew of the existence of a faithful "remnant" around the world, it was preserved, hidden away, and His Son left His glory in heaven, came into the world and gave His blood to so "buy" the world (2 Corinthians 1:2 John 5:19,2), where this remnant is.
One day, at the end of the Great Tribulation, He will return to free the Israelite "remnant" from the rebel world and install them again in their land, initiating the Messianic Kingdom, in which He will reign and enjoy His treasure.
Sometimes we find those who interpret the man as being the sinner who, discovering the treasure (which he interprets as being salvation), leaves everything that he has to be saved. This is inadmissible, because salvation cannot be bought, being a gift of God which is given to us only by faith (Isaiah 55:1, Ephesians 2:8,9, Romans 6:23, etc.). In addition, the Gospel is not hidden in a field, but it is proclaimed to the world since the beginning of the Church.
There is also a very popular interpretation of this parable, according to which the merchant would be the sinner, and the Pearl of great price would be Christ. According to this, the sinner would sell everything he has in order to buy Christ. This interpretation must be rejected as well as the false interpretation of the previous one, and for the same reason.
We hardly ever find sinners seeking salvation of their souls around the world, and the Bible also does not teach us such a thing. The sinner has nothing with which to pay for his sins, so how could he afford to acquire Christ? The merchant in the parable sold everything he had, but the sinner has nothing, on the contrary, he is dead in his trespasses and sins (Ephesians 2: 1).
Furthermore, Scripture clarifies that Christ and salvation are not for sale. Salvation is free, as we saw above.
The correct interpretation of this parable is: the merchant is the Lord Jesus Christ, and the pearl of great price is His church, that is, all those who believe in Him as the Son of God, and, repenting of their sins, receive Him as their Lord and Redeemer of their souls.
In His omniscience He saw the multitude of sinners who would turn to God, and estimated their price at a value so high that He left his home in heaven to come into this world, and shed his precious blood to redeem them from the penalty of sin to which they were subjected (2 Corinthians 8: 9). Therefore, He bought His church.
His choice of a pearl in this parable rather than another precious stone is notable, even because the pearl is only once mentioned in the Old Testament (Job 28:18) and there were other stones considered more valuable, such as the ruby.
It is likely that the reason was the nature of the pearl. A pearl is formed inside a mollusk when a foreign object that penetrates into its shell molests it. This object causes it suffering, and the clam covers it with a substance that crystallizes forming the pearl (the mother-of-pearl).
The pearl is formed slowly and, unlike other gems, cannot be polished to increase its value. If it is split, it will lose its consistency and its value, as it will no longer be a pearl.
The Israelites apparently never gave a lot of value to the pearl, and in the only mention of it in the Old Testament (Job 28: 18) it appears together with the coral. However, it was greatly appreciated by the Gentiles, so it appears in the New Testament (1 Timothy 2: 9 and a few times in the book of Revelation). The Arabs and other peoples of the East gave the pearl a symbolic meaning of purity and innocence, and considered it worthy only of royalty and high officials.
Like the shellfish, Christ also was injured in His body because of our sin (a foreign object), because He was "... wounded for our transgressions, he was bruised for our iniquities..." (Isaiah 53:5). He covers us with His white robe of righteousness: "we are His workmanship, created in Christ Jesus ..." (Ephesians 2:10), and he does not see us as we are now, but how we shall be presented to Him one day "... glorious church, not having spot or wrinkle or any such thing, but that she should be holy and without blemish.” (Ephesians 5:27).
As the pearl comes out of the sea, so the church is coming out of all the peoples of the earth, Jews and Gentiles: in Bible prophecy sea symbolizes peoples. The Lord Jesus left all the glory that was in the heavens to buy the church for Himself, and going to the description of the new Jerusalem in the book of Revelation, the future home of the church, we see the badge at the entrance o this wonderful City: its the doors are made of pearls (Revelation 21:21). It is not just a coincidence, but it was planned by Him.
The parable of the dragnet concerns the selection, which will be made "at the end of this age". This is the last parable of a series of seven, all related to the Kingdom of heaven, therefore it is a figure from the end of this era, or the "consummation of this world" according to the parable of the wheat and the tares, which looks very similar.
As that parable also teaches, there will be a work of selection between good and bad at the beginning of the Millennium, made by the angels of God, symbolized by the fishermen. While the parable of the wheat and the chaff concerns the separation that will be made of the children of God (true believers) from the children of the devil (those who pretend to be believers but are not), the parable of the dragnet is the separation to be made between the righteous and the wicked in the world (the sea).
In the middle of the tribulation period there will be preaching of the everlasting gospel by an angel to all the people of Earth, urging everyone to fear and to worship God, creator of all things (Revelation 14:6,7). As a result, at the second coming of Christ ending the tribulation shortly after, this second selection will take place:
This is hell, where they will await the final judgment that will come after the Millennium, after which they will be “cast into the lake of fire" (Revelation 20:12-14).
Nowadays it is becoming "distasteful" to preach or speak about hell from the pulpit in many of the so-called “Christian churches”. However, the Lord Jesus, who came into the world to give His precious life to save sinners, never hesitated at the idea of warning people of the terrible fate that awaits them if they continue in their sin.
The sinner needs to be alerted to the danger he is in. As someone said: "knowing the danger they are in, even those who do not have the conviction of the hereafter may repent, convert and accept the salvation that Christ offers, so they can be doubly secure: If there is nothing as the world thinks, or if the Gospel is really true, as the Bible asserts".
44 "Again, the kingdom of heaven is like treasure hidden in a field, which a man found and hid; and for joy over it he goes and sells all that he has and buys that field.
45 "Again, the kingdom of heaven is like a merchant seeking beautiful pearls,
46 who, when he had found one pearl of great price, went and sold all that he had and bought it.
47 "Again, the kingdom of heaven is like a dragnet that was cast into the sea and gathered some of every kind,
48 which, when it was full, they drew to shore; and they sat down and gathered the good into vessels, but threw the bad away.
49 So it will be at the end of the age. The angels will come forth, separate the wicked from among the just,
50 and cast them into the furnace of fire. There will be wailing and gnashing of teeth."
Gospel of Matthew, chapter 13, verses 44 to 50