"Cast your cares on the LORD and He will sustain you; He will never let the righteous fall." Psalm 55:22 And, "Cast all your anxiety on Him because He cares for you." 1 Peter 5:7

I think that The Amplified Bible opens up these two verses more fully, "Casting the whole of your care [all your anxieties, all your worried, all your concerns, once and for all] on Him, for He cares for you affectionately and cares about you watchfully."

They are those earthly cares that we get so concerned with and cause us to be anxious. Scripture tells us of their evils.
They choke the Word:
Jesus speaking in the parable of the Sower and the seeds, "And some fell among thorns, and the thorns sprang up and choked them."
Matthew 13:7
Vs. 22, Jesus explains to the disciples the meaning of the parable, "Now he who received seed among the thorns is he who hears the word and the cares of this world and the deceitfulness of riches choke the word and he becomes unfruitful."

They can weigh down your heart:
Jesus warning to watch for His coming in Luke 21:34, "But take heed to yourselves, lest your hearts be weighed down with carousing, drunkenness, and cares of this life, and that Day come on you unexpectedly."

They are an obstruction to God's invitation to come:
In His parable of the Great Supper and those invited, Jesus says, "But they all with one accord began to make excuses. The first said to him, 'I have bought a piece of ground and I must go and see it. I ask you to have me excused.'
And another said, 'I have bought five yoke of oxen, and am going to test them. I ask you to have me excused.'
Still another said, 'I have married a wife, and therefore I cannot come.'"
Luke 14:18-20

They hinder Christ's work:
The Apostle Paul to Timothy concerning being a single minded soldier of Christ, "No one engaged in warfare entangles himself with the affairs of this life, that he may please him who enlisted him as a soldier." 2 Timothy 2:4

They manifests unbelief:
In His 'Sermon on the Mount' Jesus says do not worry about food or drink or clothes, life is more than those things. (Read Matthew 6:25-34 for His word on this.) Briefly, "Therefore I say to you, do not worry about your life, what you will eat or what you will drink; not about your body, what you will put on. Is not life more than food and the body more than clothing?" Vs. 25 "...For your Heavenly Father knows that you need all these things." Vs. 32 "But seek first the kingdom of God and His righteousness, and all these things shall be added to you." Vs. 32-33

The antidote for worldly cares.
God's protection: (Reads Psalm 37:5-11)
"Commit your way to the LORD,
Trust also in Him..." Vs 5
"Rest in the LORD, and wait patiently for Him; Do not fret because of him who prospers in his way... Vs. 7 "Cease from anger, and forsake wrath; Do not fret--it only causes harm." Vs .8 "For evildoers shall be cut off; But those who wait on the LORD, They shall inherit the earth." Vs. 9

Read again Matthews 6:25-34, it also tells of God's provisions.

God's promise:
"Be anxious for nothing, but in everything by prayer and supplication, with thanksgiving, let your requests be made known to God; and the peace of God, which surpasses all understanding, will guard your hearts and minds through Christ Jesus." Philippians 4:6-7

Thank you LORD for you protection, provisions and promises. To You alone Most Holy God be all glory! Amen