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Let $f : X\rightarrow Y$ be a morphism of scheme. For any point $y\in Y$, the fibre of $f$ over $y$ is defined to be $X_y = X\times_Y Spec(k(y))$. Then the underlying set of $X_y$ is bijective with $f^{-1}(y)$.

When $f$ is not surjective and $y\in Y-f(X)$ then the underlying set of $X_y$ has to be empty set. Then what is mean by empty scheme?

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The empty scheme is the spectrum of the zero ring. –  jlk Dec 10 '10 at 5:05
The empty ringed space is the empty topological space together with the (unique) zero sheaf. –  Martin Brandenburg Dec 10 '10 at 7:56

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