Edited: It would be something like "there is some faculty member at BCC that hasn't eaten anything at the BCC cafeteria". You can think it this way: $\exists x \lnot \exists y (F(x) \implies E(x,y))$ is equivalent to $\exists x \forall y \lnot(F(x) \implies E(x,y))$ which is equivalent to $\exists x \forall y (F(x) \land \lnot E(x,y))$ and finally this is equivalent to $\exists x (F(x) \land \forall y \lnot E(x,y))$. The last equivalence holds because you can always "split" a formula like $\forall y (\alpha \land \beta)$ into $\forall y \alpha \land \forall y \beta$, in addition if you have something like $\forall y \alpha$ it is equivalent to $\alpha$ if the variable $y$ is not in $\alpha$