You will keep him in perfect peace

Isaiah 26:3
You will keep him in perfect peace,
Whose mind is stayed on You,
Because he trusts in You.

Our minds are incredibly complex - served in most part by the amazing organ called the brain. It is more than just the physical brain - the mind has a connection to our spirit, and is regarded as the source of our soul. Everyday the mind can entertain an infinite variety of thoughts. God has one advice for us, and that is to keep our minds focussed on Him.

Firstly we need to trust God to keep our minds on Him. Secondly we must will it to make our minds focussed on God. Thirdly the rewards for keeping our minds on God is perfect peace. This would be the peace described as "surpassing understanding". When we go through trouble it is worthwhile to think of God and remember His promises. When we are successful or going through blessed moment, we still need to keep our minds on God lest we fall far down.

Hide Me from the Secret Plots of the Wicked

David's prayer to God to protect him against his enemies. We know that David had many physical enemies, such as Saul and later the enemy nations which he had to fight against. But the enemy in this psalm uses secret plots, uses their tongue to lie and shoot in secret using words.
These enemies plot evil schemes rather than attack directly in battle. They "lay snares secretly" and "devise iniquities" and "shrewd schemes". So these particular enemies may be in David's court itself. In fact David did face a plot of rebellion from his son Absalom.
In any case, David's way to battle such enemies, like other enemies, is to bring it before God. He trusts that God will be just and will fight for those who are righteous and upright.

Psalm 64
To the Chief Musician. A Psalm of David.
 1 Hear my voice, O God, in my meditation;
         Preserve my life from fear of the enemy.
 2 Hide me from the secret plots of the wicked,
         From the rebellion of the workers of iniquity,
 3 Who sharpen their tongue like a sword,
         And bend their bows to shoot their arrows—bitter words,
 4 That they may shoot in secret at the blameless;
         Suddenly they shoot at him and do not fear.
        
 5 They encourage themselves in an evil matter;
         They talk of laying snares secretly;
         They say, “Who will see them?”
 6 They devise iniquities:
         “We have perfected a shrewd scheme.”
         Both the inward thought and the heart of man are deep.
        
 7 But God shall shoot at them with an arrow;
         Suddenly they shall be wounded.
 8 So He will make them stumble over their own tongue;
         All who see them shall flee away.
 9 All men shall fear,
         And shall declare the work of God;
         For they shall wisely consider His doing.
        
 10 The righteous shall be glad in the LORD, and trust in Him.
         And all the upright in heart shall glory.

Be Merciful to Me, O God, be Merciful to Me!

A plead and praise to God by David expressing his trusts and asking God for mercy. He was being hunted by his enemies, but he kept exalting God. His enemies are preparing traps for him but they got snared in their own traps. So David continues to glorify God by singing praises to Him.


Psalm 57

–To the Chief Musician. Set to “Do Not Destroy.”[a] A Michtam of David when he fled from Saul into the cave.

 1 Be merciful to me, O God, be merciful to me!
         For my soul trusts in You;
         And in the shadow of Your wings I will make my refuge,
         Until these calamities have passed by.
       
 2 I will cry out to God Most High,
         To God who performs all things for me.
 3 He shall send from heaven and save me;
         He reproaches the one who would swallow me up.  Selah
         God shall send forth His mercy and His truth.
       
 4 My soul is among lions;
         I lie among the sons of men
         Who are set on fire,
         Whose teeth are spears and arrows,
         And their tongue a sharp sword.
 5 Be exalted, O God, above the heavens;
         Let Your glory be above all the earth.
       
 6 They have prepared a net for my steps;
         My soul is bowed down;
         They have dug a pit before me;
         Into the midst of it they themselves have fallen.  Selah
       
 7 My heart is steadfast, O God, my heart is steadfast;
         I will sing and give praise.
 8 Awake, my glory!
         Awake, lute and harp!
         I will awaken the dawn.
       
 9 I will praise You, O Lord, among the peoples;
         I will sing to You among the nations.
 10 For Your mercy reaches unto the heavens,
         And Your truth unto the clouds.
       
 11 Be exalted, O God, above the heavens;
         Let Your glory be above all the earth.