Question for Theists: Why Is It Important to Begin Governmental Meetings with Prayer?

As I was thinking about this question, I thought to myself, “Anyone who wants to pray can always go down the street to a church, synagogue, or mosque. They can also pray silently. If I were a theist, that is what I would do. What’s the problem? Why do they feel it important to use the machinery of government to do this?” In the spirit of charity, I decided there must be another reason I’ve overlooked.
So the purpose of this post is to invite theistic readers to provide their answer to that question. I am especially interested in answers which focus on rather mundane meetings (such as local school board meetings, city council meetings, and so forth) as opposed to more momentous occasions (such as a Presidential Inauguration in the United States).
I am genuinely interested in their answer. I may ask follow-up questions in the combox, but I do not intend to argue with any theists who respond. I would urge other nontheists to show the same restraint for this post.