what is the truth behind the "law of attraction" and "manifestation"?

 tl;dr - It both does and does not exist.

The best way to explain this is with an example. Take a look at this:

1583124582634519826345186234518623541824816254171

What do you see here? It's just a string of numbers, right?

Well, yes.

Now I'll ask you to look for the number 9.

Since this is your given task, it's what you're most focused towards. Before this point of focus, you would have likely glossed over it. But since you "willed" for a 9 to appear, you found it.

Now, materialize the numeral zero.

The numeral zero does not exist in the above string, so no matter how hard you wish for it to appear (and no manipulation ex. inspect element, dummy), it does not exist. This is the limitation. You can play an advanced game of "Where's Waldo", but you can't make something out of nothing.

Hence the truth behind the law of attraction.