It is possible to identify Jewish prayer using several physical movements. For more on those movements, I refer you to this article found on My Jewish Learning. However, the article lacks one movement that is central Jewish, or any prayer, the lips. Without the lips, expressing words is very difficult. This is not to say anything bad of meditation, silent prayers, or internal examinations of personal thoughts. So working with the assumption that we are orally expressing our prayers, lip movements are essential. Lip movements can lead to mumbling the words, and mumbling is my topic of discussion.
There are at least three places in the Bible where we are informed about the lips. First, in Psalms 51:17 we ask God to open our lips before reciting the Amidah. Second, in Psalms 19:15, after concluding the Amidah, we ask God to accept the words that our lips have just offered. And finally in Samuel I 1:12, Hannah offers her prayer in front of Eli the Priest, and all he can see is her lips moving. Based on these three verses alone, we can see a strong scriptural support for at least moving our lips while praying, as opposed to merely reading the words with our eyes.
I can remember going to synagogue as a child and hearing all of the old men mumbling. I marveled at how they could read anything that fast, let alone a foreign language. Since then, I have come to appreciate mumbling in t'fillah. In my experience, certain words come out louder than others. It is important to note that mumbling does not mean skipping or skimming over the words. Rather, it's a recitation of the words under your breath in a way that hopefully only you are able to hear. Over time, I found that mumbling helps me significantly in my t'fillah, making it more like a conversation with God and less like a recitation. I would encourage you to attempt "project mumbles," following in the footsteps of our Biblical references. For some it will work, for others, perhaps not, but experiment and see what feels natural to you. I think we owe it to ourselves and to the t'fillot.