Psalm 42:5
5 Why, my soul, are you downcast?
Why so disturbed within me?
Put your hope in God,
for I will yet praise him,
my Savior and my God.
Psalm 42:11
11 Why, my soul, are you downcast?
Why so disturbed within me?
Put your hope in God,
for I will yet praise him,
my Savior and my God.
This refrain is obviously repeated twice in the chapter and forms the main idea of the chapter. It is basically a conversation that the psalmist is having within his inner most being. He is expressing his distress at the exile and God's punishment, yet in the midst of even this terrible time he reminds his soul to hope in God.
Even in one of the darkest times in Israel's history his hope is found in God. This displays the concept of Israel's hope well. Their hope is not a blind hope that things will work out by chance. It is a hope founded, based and substantiated in God himself. Their history reveals that even in the midst of terrible situations (ie. slavery in Egypt) God will remain faithful to his covenant. He will vindicate them.
Note the name he uses for God—my Savior (Yeshua in Hebrew, which is translated into Greek Iēsous, English Jesus). Even in the midst of the Exile the psalmist declares that God is his salvation, the one in whom his hope rests.
This same refrain appears at the conclusion of chapter 43 as well leading many scholars to believe these two chapters were originally one psalm. This appeal for vindication is precisely what the psalmist cries out for in the first part of Psalm 43.