The scriptures occasionally talk about the Lord speaking, and they sometimes describe His voice. Sometimes it is a soft voice. Sometimes it is a loud voice. But it is always a penetrating voice. It is always a voice that captivates and engages the whole soul. For me, to say out loud the words of my prayer is to make it crisp and almost visible. Prayer takes on a meaning and a life that is not quite the same when I am just thinking words or mumbling a bit. When we communicate clearly to Him, we can expect to “hear Him” more clearly in return.
Elder Jeffrey R. Holland, "To 'Hear Him' Is the Essence of the Restoration", November 8, 2020
We know that Heavenly Father hears our silent prayers or our prayers of the heart. That's a given. But I never put two and two together about the importance of praying out loud.
It makes a lot of sense though. Heavenly Father wants us to have a "conversation" with Him. We can't have a conversation without being heard, without voicing our thoughts.
Sure, He can hear us regardless, but it seems to be more important when we put in the effort, the careful thought, when we go out of our way to be alone. As Elder Holland says, it makes our prayers almost visible.
Now, we shouldn't do "as the hypocrites" to be heard of others when praying. That doesn't show Him how important this is to us. We should, as the Prophet did, retire to somewhere secluded for the intent to converse with our Father. To be alone. To hear Him converse with us.
Two things I want to point out as Joseph prayed there in the Sacred Grove.
1. He did so vocally, out loud.
2. As soon as he began, the forces of darkness tried to stop him. Now, we may not be surrounded by thick darkness that we feel "doomed to sudden destruction" when we pray but rest assured, the forces of darkness will try to stop us. Be it with a mindset to not want to pray at all, or with so many distractions that we forget to pray or even forget what we wanted to say in the first place, or with a feeling of unworthiness that we don't feel we should pray. Just know that the adversary does not want you or I to pray.
And, there's another reason to pray vocally....to show the adversary that you will pray regardless of his efforts to stop you. He can't read your mind so let's say it aloud to let him know we're not afraid of him.