Clapping of hands is a universal way of expressing emotion and praise. While worship does not have to be emotional to be valid, it usually is. The people of Skyway Assembly of God often clap while singing, especially to the faster paced songs. Some say that lifting hands is a universal symbol of surrender. But lifting hands to the Lord is certainly a biblical posture of praise and prayer.
Body language expresses the thoughts of the mind and intentions of the heart.
This is never more true than when God's people lift their hands to Him. I will lift up my hands in thy name. It's not that God is hard of hearing. While prayer and praise that is silent is just as genuine, the problem many people face is distractions. When prayer or praise is audible, people tend to stay focused on the Lord and are less likely to let their thoughts wonder.