Great peace have they
There is a quietness, a stillness, a calmness and settled assurance that comes upon every believer in Christ, for he is our peace (Eph. 2:14). This is a peace that passes all understanding (Phil. 4:7). No one has that peace except those who put their trust in Jesus, the Messiah of God. This peace is not simply the absence of aggression or war, but this peace is a calmness that entertains the patience (endurance) that accompanies our walk with Christ.
which love thy law
Every believer must have a love for the law of God, the word of God. Those who do not spend time in reading the Bible and knowing it are left to their own feeble opinions and men's philosophies. Men cannot bring peace through opinions; only God's law can bring this wonderful peace of which the psalmist speaks here. Not only are we to read the word, but we are also to love the word, and the more we read it the more we will love it.
nothing shall offend them
If we put our confidence in the word of God instead of man's ideas, there is nothing, whether it be man's attitude, his persecutions against God and believers, his changing of the word of God, his false gospel, his false Jesus, his false spirit, that can make any believer fall or stumble, which definition is found in this word offend. We cannot stumble (be offended) through false teachers no matter how influential they are, if we continue to trust the word of God for our strength and our rule of obedience to Christ. Romans 8:38-39 For I am persuaded, that neither death, nor life, nor angels, nor principalities, nor powers, nor things present, nor things to come, 39 Nor height, nor depth, nor any other creature, shall be able to separate us from the love of God, which is in Christ Jesus our Lord.