This is another place from which Peter draws on what he writes in I Peter 2:5, 9—in fact, it is almost an exact parallel. Israel and the church were both separated from the world and made holy by God. Both became God's personal property, which is what the phrase "peculiar [special] treasure" means. In addition, because of what God did—by separating them from the world—both became obligated to meet priesthood requirements.
Israel's position was conditional upon obedience. Verse 5 says, "Now therefore, if. . . ." However, Israel immediately—within a couple of days—rejected God's offer through disobedience. They rejected their privilege.
John W. Ritenbaugh
New Covenant Priesthood (Part One)
The English word translated as "jewels" in verse 17 is not entirely wrong, but it is not a precise translation of what the Hebrew word, segullah (Strong's #5459, transliterated in various ways), really means. The simplest usage of segullah is to indicate personal possession. Vine's Expository Dictionary of Biblical Words expounds its meaning (remember that we are being described):
Cegullah signifies property in the special sense of a private possession one personally acquired and carefully preserves. Six times this word is used of Israel as God's personally acquired (elected, delivered from Egyptian bondage, and formed into what He wanted them to be), carefully preserved, and privately possessed people. . . .
This is not the first time this word appears in the Bible, which distinction belongs to Exodus 19:5, "Now therefore, if you will indeed obey My voice and keep My covenant, then you shall be a special treasure to Me above all people; for all the earth is Mine." Segullah is translated as "special treasure."
The Keil and Delitzsch Commentary explains:
This manifestation of the love of God to Israel formed only the prelude, however, to that gracious union which Jehovah was now about to establish between the Israelites and Himself. If they would hear His voice, and keep the covenant which was about to be established with them, they should be a costly possession to Him out of all nations. . . . Cagulaah does not signify property in general, but valuable property, that which is laid by, or put aside, hence a treasure of silver and gold. . . .
It is helpful to note how God emphasizes segullah to impress its importance on Israel—and now us—by saying, "For all the earth is Mine." This establishes a reference point, indicating that He could have considered any people on earth as His own personal and private treasure, but He did not. Just as a person carefully and discriminately chooses his personal jewelry according to his own criteria, so He chose Israel then and chooses us now.
In I Chronicles 29:3, segullah is again translated as "special treasure," but the context provides a clear use of the term. It involves the preparations David made for the building of the Temple so Solomon could construct it. David explains that from his own personally obtained and set-aside treasure, he gave so much gold and silver.
John W. Ritenbaugh
A Priceless Gift
Reminding Israel that He owns the land and therefore has the power to make good His promises, God demands Israel's loyalty, its commitment to obey His voice. His expectation is for Israel to be faithful to the terms of the covenant. With the words "My voice," God refers to the Ten Commandments, which He "spoke" (Exodus 20:1) from Mount Sinai, as well as to the statutes and judgments (which He also spoke to Moses) recorded in Exodus and Leviticus. God reiterates His requirement for obedience in Exodus 23:21-23.
Searching for Israel (Part Three): The Old Covenant
Everything that exists belongs to God, He has the right to keep everything for Himself, but He chooses to share with human beings. He does not need to pay or repay anyone, or ask us for anything. Silver and gold are symbolic of everything of value.
Richard T. Ritenbaugh
This could be called the preface to the Old Covenant, as it presents in stark terms what the covenant is about. He lists its three main facets:
1. They were to obey His commands and keep His covenant. Recall that God chose Abraham because he would teach his children how to keep His way. The covenant set out the terms for their doing this. This was the Israelites' primary responsibility under the agreement.
2. They were to be a special treasure to Him—a people unlike all others in their relationship to God. The Israelites were to submit to God, and He in turn would help them, blessing and protecting them as only the great Creator God could. Thus, the covenant contained reciprocal responsibilities and benefits.
3. They were to be a kingdom of priests and a holy nation. This implies two additional concepts:
a. As a kingdom of priests, they were to fill the role of mediator or liaison between God and the other peoples of the earth. Just as He would work through the Levitical priesthood to the children of Israel, God would work through the people of Israel to the rest of the world.
b. As a holy nation, they would be set apart or separate from all other nations. He would require of them, as the people with and through whom He would work, that they be different, a cut above, of a higher standard. They had a responsibility to be a model for the Gentiles to observe and emulate.
John W. Ritenbaugh
Why Israel? (Part One)