Various gestures have always been used to worship and praise God: singing, dancing, arms raised, etc. David danced before the Ark of the Covenant (2 Samuel 6). Jesus used his body in various ways during his prayer: standing, kneeling, prostrating, eyes raised, hands raised; he suffered, he groaned, he sighed, he rejoiced, he sorrowed.
Christians followed his example through the centuries. Sometimes, they knelt, sometimes they stood and sometimes they prostrated themselves. Sometimes, they raised their eyes to heaven and sometimes closed their eyes. Sometimes they raised their hands and sometimes joined them.
Because the heavens and God have been represented as above, it was natural to turn upwards to pray as Jesus did. There is evidence of this form of prayer in early Christian catacomb paintings.
We raise our hands, with the palms open upwards in a giving and receiving attitude, very suitable for the Lord's Prayer. With this prayer, we praise and thank God, asking for what we need each day for the body (daily bread) and for the spirit (to forgive and be forgiven).
Priests always raised their eyes and hands when they prayed at various times in the Mass. Yet, for many years, Catholics were inhibited in bodily expression at formal prayer.
Vatican II and the use of a language we understand have enabled us to participate more fully in the Mass. We sing, we respond to the prayers of the Mass, we offer "peace" to one another, we use words and gestures of sorrow and supplication, of gratitude and joy.
And rightly so, for we are not disembodied spirits. We are our bodies and spirits. Therefore, it is natural that we use body postures and gestures that are representative of the sentiments in our hearts. That authenticates our prayer. Were we to pray the Gloria, for example, with a sad face, there'd be something wrong. It would seem that we didn't believe what we were saying or singing.
It's true that in some countries, people pray with much more exuberance, using their bodies as well as their spirits. I've been to Masses in Spanish and Afro-American churches and they truly celebrate. No one would doubt that they believe that Christ has come and saved them. We tend to be much more subdued (perhaps, reflective is a better word) but hopefully that doesn't mean that we are not praying or have less faith.
Why and since when do we hold up our hands at the Lord's Prayer at Mass? I've been at Masses in the U.S. where people's gestures are so exuberant.