In society: The ability to make someone believe something if one desires it.
As defined, influence is a kind of power, and
rightly so, firstly because the power to make someone do something if one
desires often depends on and involves influence, i.e. what one can make the
other believe, and secondly because all forms of social power much depend on
influence and ideology.
It also should be noted that in modern society very much money is
invested to gain influence, not only in politics and religion, but also in
economic markets: Extra-ordinarily large sums of money are spend on
advertisements, that not only are attempts to lure people into buying things
by false promises and silly associations, but also have a strong tendency to
trivialize public debate, and reduce it to the equivalent of sound bytes,
slogans, and poses, and to create an average public whose ends in life are
largely the having of goods that advertisments lured them into believing is
essential for their personal happiness or well-being.
For more on the logic
of influence see: Power.