Maybe the distinction between my answer here and JavaLatte's answer is too subtle to be worth worrying about, but for what it's worth:
I have no idea what the statement you quote is talking about. "Explanation" of what? "Emergent properties" of what?
But just going by the plain words:
A "brute fact" is a truth that cannot be ignored. Like, "I desperately wanted Sally to be my girlfriend, but the brute fact is that she just wasn't interested in me."
A "stance" is literally a physical position. Like we talk about a "fencer's stance" or a "boxer's stance", meaning the position in which he holds his body. In this case the word is used metaphorically. "The only honest stance" means the only position you can take that recognizes reality.
"Piety" means devotion, usually devotion to God. Like, "The monk demonstrated his piety by praying ten times a day." "Natural piety" means a piety that comes from within a person, as opposed to a fake or artificial piety. If, say, someone kneels when praying because he thinks this is just the obvious thing to do when addressing the all-powerful creator the universe, you might call that natural piety. If he kneels when praying because he saw someone else do it and he thinks this will impress the people around him with how devout he is, you'd call that artificial piety.
So putting it all together: When you consider these inescapable facts, the only response you can have that reflects reality is to accept this truth with a devotion that comes from your own understanding.
I'm still not clear what the truth that is being accepted is, but whatever.