Can someone help me make sense of this equation?

Question

I've been studying Voronoi diagrams and came upon this definition of a Voronoi region, $$V\left ( p_{i} \right )=\left \{ \vec{x}\mid \left | \right |\vec{x}-\vec{x_{i}}\left | \right |\leq\left | \right | \vec{x}-\vec{x_{j}} \left | \right |\forall j\ni i\neq j \right \}$$ in which $\vec{x_{i}}$ is the generator corresponding to the $V\left ( p_{i} \right )$ region, $\vec{x_{j}}$ is the generator corresponding to another region, and $\vec{x}$ is any point which isn't part of the set of the Voronoi diagram's generators. The inequality part I kind of get it, but what's around it confuses me.