This Psalm and the next two are Messianic Psalms. They give us a three-fold view of Christ as Savior (22), Shepherd (23), and Sovereign (24). We see in the what the LORD has done, what He is doing, and what He will do.
This Psalm is a cry of anguish which any suffering soul can identify with. However, its greater application is in Jesus Christ. It is called the Psalm of the cross because Jesus quoted from the first verse in the final hours of His Passion. By quoting this verse, Jesus was also claiming the entire Psalm as a description of Himself and His sacrifice.
Read this Psalm with a view of the cross. When you read it, you are reading about the suffering (1-21) and the victory (22-31) of the cross!