"In vector calculus, thegradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is that rate of increase.In simple terms,the variation in space of any quantitycan be represented (e.g. graphically) by a slope. The gradient represents the steepness and direction of that slope."

Gradient - Wikipedia, the free encyclopedia

I've heard of variations (i.e., change in the dependent quantity) but I'm not sure what "space" refers to. I've taken linear algebra and multi calc. so I'm familiar with the notion of a field. Does space refer to the target space of a function?