1. God’s promise and the breastpiece
17 You shall set in it four rows of stones. A row of sardius, topaz, and carbuncle shall be the first row; 18 and the second row an emerald, a sapphire, and a diamond; 19 and the third row a jacinth, an agate, and an amethyst; 20 and the fourth row a beryl, an onyx, and a jasper. They shall be set in gold filigree. Exodus 28:17-20 (ESV)
The word translated "breastpiece" means "ornament," and the priest’s role as representative was symbolized in this article of clothing.
12 And the gold of that land is good; bdellium and onyx stone are there. Genesis 2:12 (ESV)
13 You were in Eden, the garden of God; every precious stone was your covering, sardius, topaz, and diamond, beryl, onyx, and jasper, sapphire, emerald, and carbuncle; and crafted in gold were your settings and your engravings. On the day that you were created they were prepared. Ezekiel 28:13 (ESV)
19 The foundations of the wall of the city were adorned with every kind of jewel. The first was jasper, the second sapphire, the third agate, the fourth emerald, 20 the fifth onyx, the sixth carnelian, the seventh chrysolite, the eighth beryl, the ninth topaz, the tenth chrysoprase, the eleventh jacinth, the twelfth amethyst. Revelation 21:19-20 (ESV)
It appears as though the high priest’s breastplate looks back at Eden and forward to the New Jerusalem, picturing a promise of restoration to Paradise lost. (vv. 17-21)
2. God’s people and the breastpiece
21 There shall be twelve stones with their names according to the names of the sons of Israel. They shall be like signets, each engraved with its name, for the twelve tribes. Exodus 28:21 (ESV)
9 You shall take two onyx stones, and engrave on them the names of the sons of Israel, 10 six of their names on the one stone, and the names of the remaining six on the other stone, in the order of their birth. Exodus 28:9-10 (ESV)
The names engraved into the onyx stones on the High Priest’s shoulders represents the commonality and unity that we have in Christ, while the diversity of precious stones with the engraved names of the tribes represents our diverse make-up as a thing of beauty.
3. God’s placement and the breastpiece
29 So Aaron shall bear the names of the sons of Israel in the breastpiece of judgment on his heart, when he goes into the Holy Place, to bring them to regular remembrance before the LORD. Exodus 28:29 (ESV)
The gold chains secured the breastpiece next to the priest’s heart, signifying the love of God for His people, His concern for their interests, and serving as an article of remembrance before the Lord.