Exterior Derivative question

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In http://mathworld.wolfram.com/ExteriorDerivative.html,

there is a section that starts from:

Define the exterior derivative by $Dt ≡ \frac{\partial}{\partial x} \wedge t$

First of all, what does this first part quoted mean, in relation to the previous parts?

I then want to know what the rest of the section is talking about.