So 1 Peter was written during a time of widespread suffering and trial. In a moment, we will see that Peter urges believers to hunker down and endure suffering in relation to those outside the Church, to blend in. For those inside the Church, his instructions are to remain pure and be holy.
"Therefore, with minds that are alert and fully sober, set your hope on the grace to be brought to you when Jesus Christ is revealed at his coming. But just as he who called you is holy, so be holy in all you do; for it is written: 'Be holy, because I am holy.'" (1:13, 15).
What does it mean to be holy? The primary meaning of holiness is being set apart as God's, belonging to God. Since God is all powerful, all knowing, and everywhere present, there is a certain care you take with his things. You would not, for example, take something that is holy and give it to dogs (Matt. 7:6). Something that belongs to God is to be treated with respect, much as you would treat something that belonged to a king.
But in the New Testament, the word "holy" additionally took on the sense of something being pure and morally clean. It is this meaning that the word seems to have primarily here in 1 Peter. God is pure and righteous. So for you to be worthy of him, you must be pure and clean too. You must live your life in a way that is worthy of the God to whom you belong.
At this point, some Christians may object, "It sounds like you're saying we have to earn our salvation" or "What about the verse that says we're deceiving ourselves if we say we are without sin?" We will look at this faulty interpretation of 1 John 1:8 later in chapter 7. Suffice it to say, these are debates from much later in Christian history. Peter doesn't know anything about them. For him, it simply goes without question that anyone who belongs to God needs to be morally pure.
The way John Wesley and, for that matter, John Calvin, worked out these questions in their thinking was to say that, while righteous living does not earn us salvation, it naturally follows once God has grabbed hold of our lives. In other words, righteous living does not save us, but if we are saved, we will live more righteously than before. Wesley was more optimistic than Calvin about how righteously God wanted to empower us to live, but they both shared this basic understanding.
Peter and the other New Testament authors, including Paul, didn't iron out all the details. They all simply knew both that we can only be saved by God's grace and that God had certain expectations of his people. Those who did not live up to those expectations were not worthy of the kingdom of God. We will see these themes throughout the letters at the end of the New Testament, especially in Hebrews.
Here it is perhaps worthwhile to correct some common misunderstandings of what it meant in New Testament times to receive "grace."  Language of grace in New Testament times was language of patronage. Part of ancient society consisted of informal relationships between "haves" and "have nots" in which the haves gave to those in need in return for either the honor they would get in return or perhaps even for some services to be rendered.
To understand grace language, it is important to realize that there were informal expectations associated with such "gifts" (charisma) coming from "grace" (charis). Christians have tended to misunderstand how grace worked. Yes, grace was "unmerited favor" in the sense that the recipient of grace did not earn that grace and did not deserve that grace. The gift was always disproportionate to any action on the part of the recipient. Yes, there were no contractual expectations on what the giver, or "patron," would receive from the "client" in return.
But that doesn't mean that you couldn't solicit patronage, and that didn't mean that patronage didn't come with informal strings attached. The idea that you would continue to receive grace if you completely dis-graced or insulted your patron is absurd. Thus we begin to understand the comment in Hebrews 10:29 about what will happen to someone who treats the blood of Christ as some unholy, common thing and thus insults the Spirit of grace.
Despite the theological arguments of later centuries, the New Testament clearly expects Christians to live a certain way to honor the God who has given us salvation so generously. Yes, we can ask him for that salvation. It does not have to be purely a matter of his decision for salvation to be by grace. And grace could have strings attached, such as the New Testament expectation that we honor him in return with our lives.
In 1 Peter, the expectation is that we stop conforming to the evil desires we had when we lived in ignorance (1:14). This language of ignorance is one of several hints that the audience to which Peter writes is primarily Gentile. "Once you were not a people, but now you are the people of God" (1:10). Since Peter makes this comment with no hint that he is redefining who the people of God are, we have to assume that he is using these words in their normal sense, namely, that the audience has been grafted into Israel as Gentiles...
 For this understanding, I am deeply indebted to the body of work by individuals like Bruce Malina, The New Testament World: Insights from Cultural Anthropology, rev. ed. (Louisville: Westminster John Knox, 2001).