The term “people” is a somewhat colourless term by virtue of being used so often in the Bible and elsewhere. By contrast, the additional words “for his own possession” is very specific in its nuance. The point of this (quite rare) phrase is that God has laid claim to this people for the purpose of preserving them. The implication is that this people is special, very dear to God. The phrase occurs in Exodus 19:5 concerning the precious slaves whom God graciously delivered from Egypt and protected in the desert, and among whom he would shortly come to live (Exodus 40:34–38).
9 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.