Learn English – The role and the meaning of the “of”

Good question. Some contributors to this site would recommend you try Stack Exchange's English for Language Learners website, but I'm willing to attempt an answer to your question.

First, the of is a preposition in a prepositional phrase, as in your example, "of crucial importance." Let me suggest also the phrases "of moderate interest," "of weird proportions," and "of primary concern," as in

It [the statue] was of weird proportions, but it came together nicely."

It [the project] was of moderate interest to me, but I participated anyway."

It [the coat] was of bright color, but it was not garish in any way."

I guess you could say that grammatically, each of the above prepositional phrases functions as a predicate adjective. A simple definition of a predicate adjective is a word or words that modify (or predicate something about) the subject of the sentence, as in "The dress is blue," or "The dress is of blue color." Your of crucial importance and crucially important are also predicate adjectives, each of which predicates something about the subject, it.

Regarding the above sentences, if you were to ask "What kind of it was it?" you could also say, "It was weirdly proportioned," "It was moderately interesting," or "It was brightly colored."

In meaning, the two ways of describing "it" are essentially identical.

Emphasis, on the other hand, derives primarily from the nonverbal, not grammatical, realm. I'll use bold print to illustrate:

"It [the statue] was of weird proportions, but it came together nicely."

It [the project] was of moderate interest to me, but I participated in it anyway."

It [the coat] was of bright color, but it was not garish in any way."

Similarly,

"The statue was weirdly proportioned, but it came together nicely."

"The project was moderately interesting, but I participated anyway."

"The coat was brightly colored, but it was not garish in any way."

You could also put the nonverbal emphasis on weirdly, interesting, or brightly, depending on how you'd like to express yourself.

By the way, in comparing the two sets of sentences above, you could say idiomatically, "Six of one; half dozen of the other." In other words, they are two ways of saying the same thing.

Back to your sentences:

"It is of crucial importance that we make more use of technology . . .."

"It is crucially important that we make more use of technology . . .."

You could also put the nonverbal emphasis on important or crucially, depending on which word you want to emphasize. The meaning stays the same.

If you were to say either sentence in a noncommittal, monotone, unemotional way, your audience would not likely remember what you said. On the other hand, if you emphasize a word here and there, they'll likely remember that you were at least committed to what you had to say, even if they don't remember exactly what you said!