God does hear and understand our prayers, whether we speak them aloud or not. Some scriptures confirming this are:

Mark 2:8
Immediately Jesus, aware in His spirit that they were reasoning that way within themselves, said to them, "Why are you reasoning about these things in your hearts?

Ps 139:2-4
You know when I sit down and when I rise up; You understand my thought from afar. 
You scrutinize my path and my lying down, and are intimately acquainted with all my ways. Even before there is a word on my tongue, behold, O LORD, You know it all.

So we can pray out loud or silently, and there are certainly many situations where we should pray, but it wouldn't be appropriate to speak out. At other times, it can be a good thing to verbalize our prayers because it helps our concentration and even our faith to do so. Another aspect to think about is the fact that while God knows our thoughts, the Bible does not indicate that the Devil knows what you are thinking. If you are praying silently, he will know that you are praying, but won't know what; there are times when you want the powers of darkness to hear your prayers, for they will anticipate God's answer and this will help keep them from troubling us.