the exact nature of [something] => the specific characteristics of [something]

For example, one might say:

"The exact nature of nature of Dostoyevsky's greatness is hard to define."

This means:

"It is difficult to explain exactly why Shakespeare was such a great writer. "

another example:

"Nobody understood the exact nature of her illness".

This means:

Nobody could understand what kind of illness she was suffering from, and what had caused it.

In both cases it is assumed that the statement is true, the problem is that it is hard to define it.

If you google "nature of" you'll find many more realistic examples of how this is used.

I don't know if this can be translated into Russian.

Remember that there are some expressions that only exist in certain langauges. Sometimes the meaning can be translated by not the exact sentence.