In words, the formulation implies to maximize expected portfolio returns for a given maximum portfolio variance, $\sigma$ (Commonly noted as $\sigma^2$, though).
The linear restrictions $Aw\leq b$ imply the 'usual' conditions, i.e. $w_i\geq 0$, $\sum_i w_i \leq 1$ etc. Please note that your stated formulation does not include a restriction on 'full investment', i.e. you might come up with an optimal portfolio that is not fully invested. Hence, $A$ and $b$ encapsulate linear inequality conditions. Standard quadratic programming solvers let you specify equality and inequality constraints, though.
Edit:
You finally construct the matrices by combining your investment constraints, each represented by a line in $A$ and a corresponding entry in $b$. Say you want to say $\sum_i w_i\leq 1$ then this is equivalent to $w_1 + w_2 + \ldots + w_n \leq 1$ which equals $\mathbb{1}^Tw\leq 1$. Hence, you add a row of ones to $A$ and a $1$ to $b$.
Example
Say you want to invest $\geq0\%$ in each asset, but no asset should be invested at more than, say, $10\%$. this would imply
$$Ax\leq b = \begin{pmatrix}-1&0&\ldots & 0\\
0&-1&\ldots&0\\
\ldots &\ldots &\ldots &\ldots &\\
0 & 0 & \ldots & -1\\
1 & 1 & \ldots & 1\\
1 & 0 & \ldots & 0 \\
0 & 1 & \ldots & 0\\
\ldots&\ldots&\ldots&\ldots\\
0 & 0 &\ldots & 1\end{pmatrix}x\leq\begin{pmatrix}0\\0\\ \ldots\\0\\1\\0.1\\0.1\\ \ldots\\ 0.1\end{pmatrix}$$
HTH?