1 Paris: So, Spanners, how's Quercus working out in the engine room?
2 Spanners: Pretty well. I've nicknamed him "Conservative Vector Field".
3 Paris: Oh, why's that?
4 Spanners: He has potential.

A conservative vector field is a vector field v with a zero curl:

∇ × v = 0

Such vector fields can always be expressed as the gradient of a scalar field φ. This is usually defined as the negative of the scalar field:

v = -∇φ

The scalar field thus defined is called the potential of the vector field.

If you're more confused than before, rest assured that vector calculus is one of the most hilarious branches of mathematics, even if it is partially derivative.

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2016-01-08 Rerun commentary: I'd explain just a tiny bit more what a conservative vector field is, with a common example that we experience every day, but I think that would be underestimating the gravity of the situation.