Today's OT reading contains the covenant offer of God to Israel - become My people, and I will be your God (Exodus 19). This is a crucially important chapter, along with the chapters that spell out that covenant (Ex. 20-23), and the chapter that describes the acceptance of the covenant (Ex. 24).
As a part of His proposal to the people, God says, "You shall be to me a kingdom of priests" (Ex. 19:6). For years I understood this to mean, "I will make you a kingdom, and in that kingdom there will be people who are priests." But that is really not the best way to understand this language. The idea is that Israel, as a nation, will be a priestly kingdom.
The role of a priest is to stand between the people and God, to make offerings to bring man and God together. To say that Israel as a nation would be a kingdom of priests means that Israel as a nation would help bring the nations to God. This what God had already promised Abraham - that through his family all families of the earth would be blessed. Sadly, Israel more often than not failed to be holy to the Lord, much less to help other peoples become holy.
The NT uses this same language to describe God's people of the new covenant. "But you are a chosen race, a royal priesthood, a holy nation, a people for his own possession, that you may proclaim the excellencies of him who called you out of darkness into his marvelous light" (1 Peter 2:9). We must avoid the failures of Israel and be a holy people that faithful proclaims the excellencies of God to the world.