Lifting your hands is a universal and international sign of surrender. When I was young, my pastor always said something that for some reason always irritated me. Every chance he got in service he said, "everyone lift your hands" and I never did. Call it rebellion, call it disobedience, call it sin, but it was simply a boy saying why do I need to lift my hands? Ironically the answer was never given by my pastor that I can remember. It doesn't mean that it wasn't important or that he didn't think of it, perhaps I missed church that day. Thing is it wasn't till I was well into adulthood that I finally did figure it out.
There are many different reasons lifting your hands is important when it comes to worship. The first and most known reason is that it's a sign of surrender. We all know that an international signal that you are wanting to surrender is raising your hands. Many of us have either seen footage of one of the world wars where soldiers are being escorted with their hands up or waving white flags in the air. When it comes to worship it is important as a signal that you are surrendering control to God. To realize that you cannot overcome on your own and that you need help, you lift your hands to say okay God take over. Critics would say if God is God, then shouldn't he already know? The answer in short is yes, he knows but it takes us realizing that we need help to invite God to take over. We are given free will and God does not violate that...EVER. why do we have evil people? (free will to follow God or follow Satan).
Next, in order to lift your hands to surrender, you have to have faith. It takes faith to lift your hands and say, "okay God, I can't do it on my own and I need help." simply lifting your hands takes faith to say I'm lifting my hands expecting a response. Psalms 28:2 "Hear the voice of my supplication as I cry to thee for help, as I lift up my hands toward thy most holy sanctuary. This was King David saying that he lifts his hands toward heaven. Although it seems like it, it's not an act of defeat. Quite the contrary in fact it is an ultimate act of faith to say even when everything seems bleak and there is no hope, lift your hands and leave it with the only God who is able. Did you read that? HE IS ABLE. In essence it's kind of symbolic of meeting God halfway.
BUT WAIT!!! there's more! Not only is it surrendering the control, the worry, and the stress from the problem, not only is it an act of faith saying God will take care of it, but it's also an act of obedience. It's an act of worship in the fact that God, you are ultimate. You are absolute. There is none other than you. It is an act of blessing God. Look here - David lovingly calls to his faithful God: "So I will bless thee as long as I live; I will lift up my hands and call on thy name" (Psalm 63:4).
There are more than 28 verses specifically dedicated to lifting your hands in the Old Testament alone. search the word of God and look at the importance of lifting your hands in worship and obedience to God.