I'm trying to understand SVM (Support Vector Machines) and there is a single technicality I don't understand.
In Wikipedia (and several other literature), the margins are described by the equations
$$\vec { w } \cdot \vec { x } - b = 1$$ and $$\vec { w } \cdot \vec { x } - b = -1$$
Wikipedia states these equations holds with a normalized or standardized dataset. What does it mean to be normalized and why must the equations be equal to $-1$ and $1$?
I also don't understand what $\vec { x }$ is in that case? Is $\vec { x }$ the nearest point to the separating hyperplane?
Any help is appreciated.