Check cashing 'pay to the order..' ?

First let me preface this with an amusing anecdote.

There was a train accident a few years ago that I wanted to ask my wife about; just to see if she had any news on it. So I asked her: “Have you heard anything about that train wreck?”

To which she replied in all seriousness:
“You mean my family?”
So we’ve been coerced through family obligations to write a check to one of her relatives. We made out the check to her to cover some expenses that I’m not clear about. I see the electronic photocopy of the check, found online, shows that the relative clearly wrote: Pay to the order of xxxxxxx bank.

Now I’m not familiar with that type of endorsement. The relative didn’t just sign the check. Does this mean it was signed over to the bank? and not into her account? This implies to me that there is a bill (mortgage perhaps) that the bank wanted payment on. Is this a possible correct guess? What other reasons would the check be endorsed this way?

Yes, that’s how you “sign over” a check given to you to a third party, without having to deposit it and write a new check, or cash it and then pay the guy.

It is also a way to make the deposit directly to the bank. My check stamp (issued by WaMu bank with their choice of wording) reads like this:
Payable to the Order of
Washington Mutual Bank
[My Business Name]
[My Account Number]

The last two lines make sure that the check can’t be deposited to just any account at that bank, because it could be legally negotiated with just the first two lines.

So, you can’t make a certain conclusion about what your relative was doing. The endorsement is a way to pay a check over to a third party, but it’s also a legitimate way to make a deposit to your own account.