popular within the Religious Society of Friends
It is a Testament to the fundamental optimism of those who use it because, for the concepts that underlie and back the phrase are rooted in a trust that a reasonable mind, when showed the truth of a situation and of the correct thing to do, will follow that truth.
As for its meaning, the phrase is an imperative to, rather than resorting to manipulation, domination, violence, and other such methods, to go directly to those with the power over the situation and tell them the simple Truth.
Its one of those things that also requires a great deal of pure balls to pull off. Rufus Jones, A philosophy professor and founder of the American Friends' Service Committee, actually went with other AFSCers to meet with the gestapo to simply ask them to stop killing jews. It didn't necesserily achieve its full desired purpose but it is still a testimony to their method that they were left unharmed and met politely.
Speaking Truth to Power is one of the Principles behind nonviolent resistance.