Intuitively, if you're in a field, you get pulled in a different direction and/or amount depending where you are[1]. Except the meaning of the vector "pulling" on you might not be displacement of position. At a disco, for instance, you could think of the light creating a field that pulls your hair through the space of colors.

[1]Unless it's a constant field, in which case you'll feel the same pull no matter where you go.