Let's get full speed right out of the gates, here. Worship is not music, and music is not worship. There is no individual element of a Sunday service called "worship", and there is no set requirement for music to be playing in order for worship to happen.
Now that that's on the table... :)
Music is a beautiful way to enhance how God's people can reach out to Him, using words from scripture and hearts to declare some awesome things about Him. It's a powerful method to help us express things we otherwise couldn't and feel things we didn't know were there. God the Father is Spirit, so as His worshipers we aught to worship Him in Spirit and in Truth (John 4:24). More on that in another post, but suffice it to say here that music is one way to let Spirit and Truth flow together from the very same breath.
Why music? Why singing? Why does the Bible talk about it so much (Psalm 95:1; Ephesians 5:19; Hebrews 2:12; Psalm 71:23; Exodus 15:1; Psalm 105:2, and tons of other places)? Well, there's actually some scientific backing to it, but first, this exercise.
Next time you're at the dinner table with family or friends, just start singing something. You'll notice a few things right away. They're eyes will start to nervously scan the room, looking for anything to distract them from this seemingly intense thing that's going on right now. Likewise, your voice will likely become increasingly shaky as you realize how exposed and vulnerable you're becoming around these people. This screamingly unscientific exercise is enough to show that music exposes something beyond, within, underneath these layers of protection we put up. Music puts us in our undies...but hey, the great King David knew all about that (2 Samuel 6).
Now, the science, with special thanks to Science Mike of The Liturgists Podcast's episode 17. "Worship is crazy, neurologically speaking, and it's especially crazy when it involves music...When we attach music to worship, it's more neurologically powerful, it's more potent". Science Mike goes on to describe how active our brains are when we listen to music in general. Not just the parts of the brain that process sound, but also the left temporal lobe (where language happens), the right temporal lobe (for creativity), and all across the corpus collosum (the bridge between the left and right hemispheres). To top it off, this is amplified to another level when adding in the element of participation. And yes, when we all sing songs together in a worship service, that's quite the participatory experience. They get into more detail, but you get the point.
Through it all, music enhances our ability to worship God. To see Him, to express ourselves towards Him, and to magnify His name. Contemporary music, traditional music, vocal music, ancient music - it's all the same. Let's sing a song to our Maker, and let our brains and souls light up in worship.