In Hebrew culture, thirty pieces of silver was the price paid to the master of a slave if his slave was gored by an ox:
“If the ox gores a slave, male or female, the owner shall give to their master thirty shekels of silver, and the ox shall be stoned” (Exodus 21:32).
A prophetic reference to the thirty pieces of silver given to Judas Iscariot is found in Zechariah 11:13. This is the amount of money that Zechariah was paid after his work as a shepherd. He asked his employers to pay him what they thought he was worth. They gave him thirty pieces of silver, which he sarcastically calls a “lordly price” because it was such a small amount. The employers meant to insult Zechariah with this amount of money. Returning the insult, God tells Zechariah to “throw it to the potter,” and Zechariah tossed the money into the house of the Lord to be given to the potter:
“Then the Lord said to me, “Throw it to the potter”—the lordly price at which I was priced by them. So I took the thirty pieces of silver and threw them into the house of the Lord, to the potter” (Zechariah 11:13).
These actions are an accurate and detailed prophecy, for when Judas Iscariot bargained with the chief priests to betray the Lord Jesus, he asked, “What are you willing to give me if I deliver him over to you?” The chief priests then counted out for Judas “thirty pieces of silver” (Matthew 26:15). That’s all they considered Jesus to be worth.
Later, Judas was overcome with guilt for betraying Jesus, and, fulfilling Zechariah’s vivid prophecy, he threw the thirty silver coins into the temple (Matthew 27:3–5). The Jewish leaders used the thirty pieces of silver to buy a field from a potter, again as Zechariah had predicted (Matthew 27:6–10). It was in that field that Judas hanged himself.
The significance of the thirty pieces of silver is that this paltry amount - the price paid to the master of a slave to compensate for the death of a slave - is all the chief priests considered the life of Christ Jesus to be worth.
Edit: I found the references to the 30 pieces of silver and the connection to the prophecy in Zechariah 11:12 from the Catholic Encyclopedia, part of which says this:
St. Matthew is the only Evangelist to mention the sum paid by the chief priests as the price of the betrayal, and in accordance with his custom he notices that an Old Testament prophecy has been fulfilled therein ( Matthew 26:15 ; 27:5-10)... Matthew sees the fulfillment of the prophecy ascribed to Jeremias (but found in Zechariah 11:12): "And they took the thirty pieces of silver, the price of him that was prized, whom they prized of the children of Israel. And they gave them unto the potter's field, as the Lord appointed to me" (Matthew 27:9, 10).
The article goes on to say how a field was purchased with “the reward of iniquity,” that it was “bought with the rejected price of his treachery” and goes on to discuss the motives/reasons for the betrayal by Judas. It asks the question, why was Judas “tempted to such gross ingratitude for such a paltry price?” This is the connection between the value placed on the life of a slave (in Exodus 21:32), and the prophecy about the thirty pieces of silver in Zechariah 11:12.
“The same Evangelist [John], as we have seen, tells of an earlier intimation of Christ's foreknowledge of the betrayal (John 6:71-2), and in the same chapter says expressly: "For Jesus knew from the beginning, who they were that did not believe, and who he was, that would betray him" (6:65).”
It is worth pointing out that the thirty pieces of silver was no random amount. It was prophesied long before the event took place.
P.S. The thirty pieces of silver had a value of 120 denarii. Back then, a labourer would be paid one denarius for a day’s work.