The relationship between randomness and compressibility only exists when we talk about the source, or the hypothetically infinite string of outputs from the source. For instance, we know that a source that outputs either 0 or 1 with equal probability is random and that the stream it produces is "incompressible" (in the sense that, for any fixed compression algorithm, in the limit as the length of the stream goes to infinity, the stream cannot be compressed by that compression algorithm: the average compression ratio is $\le 1$).
Any finite string can be compressed down to nothing, if you let me pick a suitable compression algorithm; i.e., for any finite string $y$, there is a pair of algorithms $c$ and $d$ which compress the string to nothing, and decompress nothing to the string. These algorithms are easy: $c(y) = \epsilon$ and $c(x) = 0x$ for all $x \neq y$, whereas $d(\epsilon) = y$ and $d(0x) = x$. The compression ratio is bad for most strings, but you've just compressed any finite string -- including one generated by a random source -- down to nothing.
You can talk about compressibility for specific compression and decompression algorithms in the context of random finite strings, but not about limits of compressibility in general terms.
Another way to understand this is that there's no such thing as a random finite string.
As for how this addresses the question:
Suppose I have a compressed file and it is not possible to compress it more without loss of information.
I demonstrate that this cannot hold for a finite string.
We say that this file is random or pseudorandom.
Then we conclude that such a thing does not exist.
So, if the randomness means not comprehensible and not compressible,
For producers and the potentially infinite streams they produce, I'd grant that this is a reasonable interpretation
I don't understand why this file is, at the same time, information that my computer and I can understand.
Because the file isn't a potentially infinite random stream, and represents a discreet entity which still contains plenty of information.
This file could be a book that my computer can show to me and read, and I can read and sum it ...so, it is really randomness?
It is not, as outline above.
Note: I understand that if I can make a summary of a text or define it with less words, that not means that it could be possible to get all the information of this book again, of course but this book is not random for me.
Neither is any string, since what (I think) you are describing is a valid way to interpret the result of applying a compression algorithm to any finite string: it's a digest, or summary, for which there is indeed some algorithm that will losslessly convert it back to its original form.