Principle number 14 of Basic Elements of Islam: The prayers involve moving together in time. When Muslims pray, they all face the same direction, they bow down, get on their hands and knees, and put their face on the mat, all in unison, and then rise back up. Again and again.
When people move together in time, whether dancing or marching or praying, it creates a physical and emotional bond between them. That's why all military training involves close-order drill (marching in unison), even though it has been a long time since military groups have actually marched into combat. There is no longer a need for the skill, but military training retained the practice because it is so effective at creating a strong feeling of unity between soldiers (read more about that).
The same is true of any physical movements people make in unison. So the method of prayer in Islam helps Muslims feel unified with each other.