prepositions - Meaning and usage of "be of"

I see such sentences all the time and I'd like to learn more about their grammatical structure (e.g. how they are described in grammatical terms), their meaning and how to use them in different contexts.

Please let me know whether I can be of help.

The part that I am interested in learning about is be of.

There is a similar question here but the questioner was asking only whether it was correct or not, but I would like to learn the meaning more broadly as I described in my opening sentence.

Answer

As far as I can tell, there are only a limited number of nouns that work with "be of". I would classify them as idioms. I am listing the most common ones I can think of, where commonness is judged by Google Ngrams. I have grouped them into sets of near synonyms. There are

be of use,
be of help,
be of aid,
be of service,
be of assistance;

these idioms mean that something/someone can be used, can help, can aid, can serve, or can assist. There are also

be of relevance,
be of importance,

which mean that something is relevant to/important for the current subject of discussion.
Also,

be of value,
be of benefit;

these mean that something is valuable, usually with respect to the current subject of discussion. Also

be of interest,

which means that something is interesting.

And for a slightly different "be of" idiom, there is

be of age,

which means that someone has reached adulthood.

If you are learning English, it should be fairly easy to figure out what one of these constructions means. But I would suggest that if you use this construction, you should treat it like an idiom, and memorize the specific phrase(s) you want to use. Many nouns describing attributes, like "security" or "tact", cannot be used with "be of". (Google books gives a few instances for "be of security"; it seems to have been used occasionally in the 19th century, but it sounds very strange today.)