WHAT DOES 1 PETER 2:9 MEAN WHEN IS REFERS TO BELIEVERS AS PECULIAR PEOPLE?

Let's see what Peter is talking about:

1 Peter 2, 2-10: As newborn babes, desire the sincere milk of the word, that you may grow thereby: If so be you have tasted that the Lord is gracious.

To whom coming, as unto a living stone, disallowed indeed of men but chosen of God, and precious, you also, as lively stones, are being built up a spiritual house, a holy priesthood, to offer up spiritual sacrifices, acceptable to God through Jesus the anointed one. Wherefore also it says in the scripture: Behold, I lay in Zion a chief corner stone, elect, precious: and he that believes on him shall not be confounded.

Unto you, therefore, who believe he is precious: but unto them who are disobedient, the stone which the builders disallowed, the same is made the head of the corner, and a stone of stumbling, and a rock of offense, even to them who stumble at the word, being disobedient: whereunto also they were appointed.

But you are a chosen generation, a royal priesthood, an holy nation, a purchased people [bought and paid for by the blood of the Lord Jesus]; that you should show forth the virtues of him who has called you out of darkness into his marvellous light: Which in time past were not a people, but are now the people of God: which had not obtained mercy, but now have obtained mercy.

First if you will notice my translation the word "peculiar" should be "purchased".... 

Also Peter quotes an O.T. verse that speaks to Israel...

Exodus 19:5-6: Now therefore, if you will obey my voice indeed, and keep my covenant, then you shall be a peculiar treasure unto me above all people: for all the earth is mine: And you shall be unto me a kingdom of priests, and an holy nation.

Indeed, this is our standing as those who have been grafted into the olive tree - Israel and have become a part of the commonwealth of Israel, now members of the house of God; His congregation as in the Messiah [King] of Israel; who is the representative man of Israel. We in him are the Israel of God - as Peter has referred to - "a chosen generation, a royal priesthood, an holy nation, a purchased people; that you should show forth the virtues of him who has called you out of darkness into his marvellous light"

So as Israel of old was to be a witness for Yehovah to the Gentiles [world] and failed; and not only failed but rejected their own Messiah; and in rejecting him have be cut off from Israel.

Now the only ones who can be a part of the Israel of God are those who believe and accept the teaching of the lord Messiah Jesus whether Jews or Gentiles, we are all on the same plane, all have sinned.

Those who believe in Jesus as the Messiah - God's anointed one are grafted into the olive tree - God's Israel - that Jesus represents and is the King of. [Romans 11]