Psalm 22 is of profound significance to anyone who loves the Liturgy of the Hours. Here we learn from the example of Jesus to use the psalms as our most personal prayers, to express to the Father our sorrows, our petitions, our thanks and our praise. Sacred Scripture is not just a thing to be studied, but to be prayed. That is what Jesus did; that's what we should do.
Yet, in praying this psalm as part of the Church's liturgy, we are doing something even greater. Acting as members of Christ's body, we are praying this psalm through Him, with Him, and in Him. Sound familiar? Of course. Like the mass, the Liturgy of the Hours is something we join ourselves to with the Church universal. In this case we don't offer the sacrifice of Christ's body and blood, but we do offer the sacrifice of His--and our--praise to the Father. Our offering is imperfect, but joined to, and subsumed by, His perfect praise, it becomes a great and holy thing.
Most of us realize how mind-boggling it is for us unworthy shlubs to be able to participate in the Holy Mass. It makes no sense that Jesus wants to come to us in this way, but we're glad that He does. It wouldn't be a bad idea to cultivate that attitude towards the Liturgy of the Hours as well.
Pope Benedict gave a meditation on the prayer of Jesus on the cross, "My God, my God, why have you forsaken me.?" which also deals with Psalm 22 as a whole. If you like the quotes from the preceding news agency link, you might want to read the entire talk on the Vatican website.