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A '''field''' is a spacial distribution of some quantity of interest. If a field is known, effectively the quantity is known at every location within that field (we say the field '''evaluates to''' something at that point). For example, there is a temperature field in your house, which might evaluate to 25 degrees on the armchair in the living room, 20 degrees on the bedroom floor, but only 15 degrees somewhere on the balcony.
A '''gradient''' is how quickly something (a field variable, i.e. a quantity that can be represented by a field) changes with respect to distance. The most notable example being the slope of the ground. On a hill, the height varies with position, so we can define a height gradient. If the height gradient is large, this means the height changes quickly with respect to distance, so we say (the slope of) the hill is steep.
The '''aspect ratio''' of something is (roughly) the ratio between the length and the width. It describes how slender or stubby something is. A square has the aspect ratio of 1 because its width is the same as its length. A (new) pencil has a larger aspect ratio than a piece of rubber.
= What a wing actually does =