We received a copy of the wife's great uncle stating she (my wife) is listed as a beneficiary to 10% of the residuary estate. Is there anything we should be doing, or just sit back and relax? We were a bit surprised to hear she was one of the beneficiaries, so we aren't expecting anything really, but her brother is also listed...and well, it could get "messy". We don't know anything really about her uncle's finances, so we really have no clue what to expect. Again, we don't expect anything really, but how do people (that aren't really in the know about the details) know that the executor of the will is doing exactly that? This is "family", but not family we really see, or even "know".

My wife and I really don't care, as it came as a surprise. We aren't looking to hire an attorney or whatever, really just asking for her brother's sake...

These things take time. A clean one can still take a year or more. It really depends on how many things there are to sell/transfer and the executor. Some executors are on top of it. Most are not because they have a life.
Also, some accounts can't transfer until all beneficiaries complete a form, and not all of the beneficiaries are quick to respond.

I have seen larger estates take up to 2 years.

You will want an attorney on here for help, but the word residual and 10% seems to me like a very small amount. Meaning tell the brother to expect very little and about 2 years. The estate will have to process everything (bills, accounts to beneficiaries, it's own tax return or two) before sending out the residual.

As for the executor, he can be sued if he messes up (also held responsible by courts), so they are usually good about doing the moral thing.

"Residual" in the context of a will is a legal term of art meaning the property/assets left over after specific bequests are made. For example, I bequeath my guns to my brother-in-law and the residuary of my estate to my wife. My wife gets all my stuff (except the guns). There's no way to know what the 10% is...could be little, could be millions. It has nothing to do with describing something as "small" or "de minimis".

Look at the section or language before the residuary language and see what specific bequests are made.

I would reach out to the named executor and find out if they've retained an attorney to probate the will and if so, stay in touch with that lawyer and monitor the process. At some point, they will have to file an inventory with the court listing all probate assets (will not include non-probate assets like life insurance proceeds).

*This is assuming the decedent is in Texas and this isn't legal advice specific to your case.