When you pay attention to someone, you align your mind with that of the other person. This means you alter your mental and emotional processes according to your internal model of the other — in terms of her experiences, point of view, intentions, thinking, feelings, desires, will, actions, and/or perceptions. The better you can do this, the better you are able to pay attention. Such alignment is never total. You do not give up all sense of your difference from the other, and usually not permanently your own viewpoints which would be discordant with hers. But you are usually changed by this to some degree.
When you pay attention to someone, that means you align your mind with theirs, which also means you temporarily reshape your mind to resemble theirs in some way. To a degree, this always leaves traces; you are changed. To the extent of that change, what you then do is done under their influence.
This reshaping, and therefore influence can be stylistic, attitudinal, emotional, insight-related, conceptual, meaning-connected, factual or following the direction of their own attention in some way. On occasion, we refer to all of these as examples of influence