"Until" and past perfect

Having seen one sentence in "Practical English Usage" by M.Swan (a very popular grammar book), I was really puzzled.

I waited until the rain had stopped.

The past perfect is generally used to show that one past action was completed before the other one, but here, trying to analyze the sentence, we can't say that first the rain stopped and then she waited. I can't grasp the use of using the past perfect in this sentence.

Why does this sentence use the past perfect?

Answer

The past perfect is used to emphasise completion of a past action. Example:

I arrived home after my wife had gone to bed.

In other words: "My wife went to bed. Sometime after that I arrived home."

In your sentence, the speaker is using the past perfect to emphasise the following:

It stopped raining. Sometime after that I stopped waiting (because I was sure that the rain had stopped.)

If you do not wish to emphasise the point about the rain stopping, it is perfectly ok to say:

I waited until the rain stopped.