Seeking better understanding of Fourier transform?

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I'm quite confused on the one part of the Fourier transform. I don't understand what is the term $\left(u*x + v*y \right)$ mean. I mean $u$ and $v$ are the axis for frequency domain and $x$, $y$ are the axis for time domain, but why do we multiply them, I see how they derive it, but what is the actual meaning of it? I don't quite the meaning from the derivation. If possible could you explain?