When we want to talk to God, or make a special request to Him, we can do something called dua. Raising our hands during dua is a way of showing that we are asking God for something very important to us. Just like when we ask our parents for something, we might hold our hands up to show them we really, really want it.
By raising our hands during dua, we are also reminding ourselves to respect God and to ask for His help humbly. We are asking for something from someone very powerful and important, so we want to show that we understand that and are grateful for any help we receive.
Some people might not raise their hands during dua when they are praying, but it's a personal choice based on what makes them feel most connected to God.