(abstract) This place; this location.
An Alzheimer patient's here may in his mind be anywhere he called home in the time he presently re-lives.
(abstract) This time, the present situation.
Filler after a noun or demonstrative pronoun, solely for emphasis.
John here is a rascal.
Filler after a demonstrative pronoun but before the noun it modifies, solely for emphasis.
This here orange is too sour.
(location) In, on, or at this place.
Flu season is here.
(location) To this place; used in place of the more dated hither.
Please come here.
(abstract) In this context.
Derivatives can refer to anything that is derived from something else, but here they refer specifically to functions that give the slope of the tangent line to a curve.
At this point in the argument, narration, or other, usually written, work.
Here endeth the lesson.
Used semi-assertively to offer something to the listener.
Here, now I'm giving it to you.
Used for emphasis at the beginning of a sentence when expressing an opinion or want.
Here, I'm tired and I want a drink.