What does 1 Peter 5:7 mean?

This verse concludes the thought begun in verse 6. Christians must humble themselves under God's mighty hand, trusting Him to exalt us at exactly the right time. We must quit the work of seeking our own glory in order to accept the work of serving and submitting to others. Then, when the time is right, our God will use His mighty hand to exalt us.

These are words of great encouragement, and maybe conviction, for those struggling to submit to harsh human authorities. It speaks to those serving year after year with little recognition. It encourages those providing for others of limited power or value in society. Natural human fear tells us we are wasting our lives, we are on the wrong path, that our choice to serve in humility without obvious reward is evidence that we may be worthless, after all.

Peter writes that we should take that fear and cast it—throw it—onto our Father God. In fact, he tells us to take all of our anxieties, everything that worries us, and to give it to the God who cares so deeply for us. This is not a promise that God will fix everything which worries us. God is not obligated to follow whatever script we write for Him. It's a promise that the mighty God will receive our worries, and care about them. He will carry them for us. He is trustworthy to handle them in the way that is best.

Peter's words are a command. It is not God's will for His children to continue to live under those burdens. Believing that God is mighty and cares for us should result in our regularly handing over our worries to Him.