In recent article of PM the memcomputing is presented. But I did not understand how it works, according to the text.
What is the general principle of work for this
memcomputing? How it is done in hard-ware?
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It doesn't work. I am paraphrasing Scott Aaronson in this answer, whose article on the subject gives more details.
They claim to have some way of solving the subsetsum problem efficiently. The basic gist being that they encode all of the numbers in the instance as electrical signals, and then throw all the electrical signals together in to a big melting pot. They then measure the output signal and try to find whether it contains a signal corresponding to a solution.
However, this requires an exponentially precise signal (to be able to figure out whether the particular frequency/signal you want is there) so it isn't really a viable approach to solving $NP$-complete problems. The article claims that this is likely to be resolved in the future and that the general principle of memcomputing might one day become viable but I think that claim should be taken with a grain of salt. It seems that whatever trade-off you make, be it time, energy, memory or precision, you always end up hitting some barrier that requires exponential resources.