Your question is a good one. Moreover, in light of the abstractness of the first few verses of chapter 1, your question is quite natural and understandable, since the verses give us little by way of concreteness but plenty by way of nebulousness!
Nevertheless, by first, defining the key terms in verses 3 and 4, and then second, by interpreting those two verses in the context of verses 1-12 as a whole, we might be able to determine what the "divine nature" meant to Peter and, by extension, what it means to us.
- God's power: the source and resource of the wherewithal for living a godly Christian life
- Knowledge: progressive, intimate, and relational, friend-to-friend knowledge
- God's glory and excellence (or virtue): the outshining of His sui generis character and infinite integrity through the instrumentality of His creation, particularly His vessels of clay (i.e., us; see Romans 9:23 and 2 Corinthians 4:7).
- Partakers: those who appropriate existentially and progressively God's communicable, shareable attributes
- God's nature: God's communicable, not incommunicable, attributes, with the latter being, for example, omnipotence, omnipresence, and omniscience, and the former, those attributes laid out by Peter in vv.5-7.
In the larger context, then, Peter develops a contrast between our old, sinful nature (à la Paul in Romans 7, 8, and 13) and our new-birth nature. Both natures are characterized by an evolution or progression. The latter nature actually de-volves in a downward spiral of corruption and death, both spiritual and physical (see, for example, Romans 5:14,17,21; 6:16,21,23; and 8:6).
The latter nature, however, evolves in a progressive, sanctified direction; first, because of God's induement of the wherewithal to live godly lives, and second, because of our ongoing decisions to live according to the principles laid down for us in the faith, once and for all delivered to the saints (v. 1; cf. Jude 1:3).
Our new life in Christ is acted out in stages, as God, with our permission, "adds" more and more Christlikeness to our characters (e.g., the building blocks of virtue, knowledge, self-control, endurance, godliness, brotherly/sisterly affection, and love).
As God's children, we have retained His image (Genesis 1:26), as does all of humankind. Though that image is spoiled by sin, it is redeemable. The image of God and the nature of God, however, are two different, albeit related, things. First, God's nature has never been, is not, nor ever will be spoiled or sullied, as was God's image in us. Second, whether believer or unbeliever, we still relate to God through our minds, emotions, and wills. To the believer, however, through God's powerful endowment in us, who walk not according to the flesh but according to the Spirit (Romans 8:4), we are enabled to live godly lives. Consequently, God's image in us is, in fits and starts, inexorably restored and re-created in us incrementally, step by step, as we fulfill our duties as God's bondslaves (v.1).
In other words, as we partake of, or appropriate, more and more of God's infinite, inexhaustible nature, we are continually sanctified, or set apart, for love and good works (vv.5-8,10; cf. Hebrews 10:24). Our spiritual maturity is a consequence of willingly, through God's enablement,
"applying all diligence"(v.5)
"practicing these [qualities],"
so that God imparts His character traits to our lives. In other words, we are to
"work out [our] own salvation with fear and trembling, for it is God who works in us both to will and to do of His good pleasure" (Philippians 2:13,14; cf. Peter's concepts of usefulness and fruitfulness in v.8).
God's character traits, or attributes, are the building blocks I listed above (viz., virtue, knowledge, self-control, endurance, godliness, brotherly/sisterly affection, and the capstone, love), which are laid on the foundational cornerstone of "the faith" (v.1). We can think of God's work as a masterpiece which God desires to make of us through His granting of the necessary enduement (v.3), and His granting of precious and magnificent promises (v.4), all for our benefit and His good pleasure.
In summary, then, how do we become partakers of God's nature? In short, by simply appropriating, or making our own, all that God through His power and promises is willing and able to mediate to us through Jesus Christ. God may invest His power and promises in mere clay vessels, but those vessels can become, through His molding and shaping,
"pottery for noble purposes" (Romans 9:21).
This transforming process requires everyone who confesses the name of the Lord to
- turn away from wickedness (2 Timothy 2:19b)
- clean himself of wickedness (ibid., v.21a).
For in doing so, each Christian will become
"an instrument for noble purposes, made holy, useful to the Master and prepared to do any good work" (ibid., v.21b).