To describe a plane in the $n$ dimensional space we can use the following formula
$$\boldsymbol{w}^T\left[\boldsymbol{x}-\boldsymbol{a} \right] = 0.$$
This is equivalent to say that normal vector $\boldsymbol{w}^T$ is perpendicular to any vector in the plane $\left[\boldsymbol{x}-\boldsymbol{a} \right]$, in which $\boldsymbol{a}$ is an arbitrary point in the plane. Note, that $\boldsymbol{a}^T\boldsymbol{b}$ is the matrix notation for the dot product. The vectors $\boldsymbol{a}$ and $\boldsymbol{b}$ are perpendicular to each other if the dot product $\boldsymbol{a}^T\boldsymbol{b}=0$.
If you expand this formula you obtain:
$$\boldsymbol{w}^T\boldsymbol{x}-\boldsymbol{w}^T\boldsymbol{a} = 0,$$
in which $-\boldsymbol{w}^T\boldsymbol{a}$ is just a constant scalar which was called $b$ in your expression.