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Unless otherwise defined in bylaws or some other code, a quorum is a majority of the members and the minimum number of members necessary to transact legal business at a meeting. Beyond that, it gets complicated.
There is no exact and perfect number for a quorum, and each organization should carefully consider its nature and future in writing that section of its bylaws. My university fraternity in the 1960s had a quorum of 90% of the members, and in the five years I attended meetings, we never failed to get a quorum; in this organization it was clear that meetings were important and members were expected to be at them. On the other hand, my wife was the first President of a non-profit organization called the Fresno Lupus Foundation and in that group the quorum was set at a majority of the members. At its first event it signed up about 250 members, almost all of whom had come to hear the famous physician speaker and did not plan to be active members. Anyway, this group never did get a quroum to have a meeting for several months, in spite of its having generated a lot of money to use. Needless to say, that group dropped its quorum to a reasonable number. The English House of Commons, by the way, has thousands of members, seats for only a couple of hundred, and a quorum of about fifteen.
There isn't anything magical about the idea of a majority as the quorum, although by common law in the United States it is the default definition. Therefore, the answer to your question is "nothing exactly" in general, but "something exactly" as defined in your bylaws.
I think it is the original "understanding" that was incorrect.
In the absence of a specific statement that linked the quorum to the total number of possible members, then the "default" meaning of quorum is more than half of the members. However, "members" refers to people who are appointed and continue to serve. If illness, for example, forced the resignation of several members so that only five members remained on the board, then the quorum would be three. What you asked about is the meaning of quorum in parliamentary law and parliamentary procedure manuals.
An important point is that there is no "magic" number for a quorum that applies to all groups. Each group has different circumstances. The quorum for the English House of Commons is 15 out of thousands of members. If your advisory committee is a statewide group constituted with busy people in various professional positions (for whom schedule conflicts are common), most parliamentarians would probably advise a lower quorum number. Conversely, various political and/or expertise dimensions of a committee's composition could make an even larger quorum. In my university fraternity years ago, we had a quorum of 90% of all the members for all meetings (and in the five years I was in the fraternity getting my BA and MA degrees, we never failed to get a quorum). There is a "default" meaning, as described above, to cover cases generally.
It is the consituting authority that sets the definition of quorum,
which is why you should consult the Governor's Office. Since your
authority derives from his executive authority and since your ability
to advise and influence his decisions depends on his confidence in the
group, you should be sure that your understanding is in good
synchronization with his/hers (I'm embarrassed on election day, even
2000 miles away, not to know who is Governor of Louisiana).
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