Well first of all the word medium is exactly what the person does.
It is a way to communicate through a machine or person able to bridge the gap between you and another. In this case a person.
The medium interprets the "other side" to the people who cannot sense it.
May I expand... 
I totally understand what I mean when I use the word 'medium' - I've deliberately not defined it here because I'm interested in what it means to others.
It's a subject I've been trying to progress for many months but mostly I've found that folks simply do not, or can not, say what it means to them personally. And I can tell from the little that folks do say, that it's something different to the meaning I imply....
If I take "The medium interprets the "other side" to the people who cannot sense it." then I'd ask is that what you understand or a general definition?
And I'd also ask what you mean by "interpret" and "the other side"....
