Your health and well-being are of paramount concern to us. What does 'of' mean here?

Welcome to the site. Good question!

This is a fairly unusual sentence construction in English. It's a structure that's hardly ever used in contemporary, colloquial speech, except in fossilised idioms like:

"of paramount concern" or "of utmost importance".

It's the possesive/genitive of, the same as the of in a phrase like "the Queen of England".

You could think of how this phrase originated like this:

1. A cause of concern
2. [Add an adjective] a cause of paramount concern
3. [turn the whole phrase into another adjective] a situation of paramount concern

The translation into simple English would be:

Your health and well-being are very important to us

Phrases constructed like this are only used in formal or academic writing generally, except in parts of Southeast England, where they're sometimes used in conversation.

"of paramount concern" is an prepositional adjectival phrase (an adjunct) and describes the [fundamental] nature of "Your health and well-being"[1].

"To us" is a free modifier (adverbial) that modifies the whole clause. The example can be written

"To us, your health and well-being are of paramount concern.

[1] Compare, as in my comment above, "The statue is of gold".

Recall: "of" is a preposition, and prepositions establish relations between nouns. Sometimes, this gives rise to adjectives in the form of phrasal attributives, which an adjective could replace.

There is a tendency to call a phrase an adjectival phrase when that phrase is functioning like an adjective phrase but is not actually headed by an adjective. For example, in "Mr. Clinton is a man of wealth", the prepositional phrase of wealth modifies a man in a manner similar to how an adjective phrase would, and it can be reworded with an adjective, e.g. "Mr. Clinton is a wealthy man". A more accurate term for such cases is phrasal attributive or attributive phrase.

— Adjective Phrase > Adjectival Phrase - Wikipedia

Let us revert to the question.

Your health and well-being are of paramount concern to us.

Here, as in the previous cases, "of paramount concern" post-modifies "health" and "well-being" with no adjective heading the phrase—it is a phrasal attributive. Again, we may lose meaning by using a one-word adjective in place of "of paramount concern" as a pre-modifier. Therefore, we use the long phrase, which is just a phrasal attributive or attributive phrase.

If one is to really 'dissect' the sentence, think of it like this: the actual expression is to be a matter of concern, which is similar to other expressions that have been indicated in the other answers and comments (like for example a matter of importance).

Now paramount simply comes as an enhancer of concern. For this reason, grammatically, you cannot replace of with a and obtain an identical phrase, the connections between the words are changed. As for the meaning, if you apply this replacement, the sentence does not change its message.