Our thoughts and reliance should be centred on God rather than worldly things or ourselves. This gives us courage, peace and strength even in face of adversities. NIV translations phrase it slightly differently. "You will keep in perfect peace those whose minds are steadfast, because they trust in you." Perfect Peace" is not just absence of trouble, but a deep, abiding tranquility from God.
"Mind is Steadfast" indicates a mind that is focused, committed, and leaning on God, not wavering.
"Because they trusts in You" is in fact the foundation of this peace. It is out complete reliance and confident in God and God alone.