What is the meaning of the word 'power of death' which Satan was holding as in Heb 2:14.?
The Devil is considered a prince of a kingdom. To be a prince he must have some kind of power that he wields over his subjects. If we said a king has the power of wealth, we mean he has a lot of money and that he exerts a lot of influence by it. In the same way the 'power of sin' or 'power of death' is something one can have and exert influence with. The Devil having introduced sin into the world and through sin death, became a prince of the world having a lot of destructively powerful sin and death in himself. Like a disease, the Devil, with the power of death, causes sin and death to spread through his influence. He according to this power works his desire to destroy and kill. He by his daily temptations increases death in the world, a world under his power as a result of being made subject to death.
The Devil by tempting Adam and Eve brought all men under a power of death
He is a prince over the kingdom of the world which resulted from death entering into it
Although there may be nothing legitimate about his power of sin and death, he nevertheless has great power in his rebellion as the prince of this world and is in that sense like a powerful Lion:
Therefore to conclude with a pointer from the obvious beginning, God said the moment Adam ate from the fruit he would die but this could not have been primarily physical as he did not die. Also that they felt ashamed, hid from God and this proves they did die inwardly. The bible does not treat physical death as serious as spiritual death anywhere.
The power of death is the legal power of the accuser, which is what Satan means. In my opinion he could hold mankind prisoner under the curse of the Law of Eden. This is why the grave has "bars and gates," pictorially speaking, and why (according to some Christians) those gates shall not prevail against the Church, which they say has the power of the legal Advocate. He bound the "strong man" and released all the Old Testament believers.