From where does positive semidefinite thing came

Question

From Boyd & Vandenberghe's Convex Optimization:

As I understand, all $x_i$ are scalar. So, when it says $A(x) \preceq B$, it should mean elementwise inequality. Thus for $B - A(x)$ matrix, all elements should be $\geq 0$. From where does positive semidefinite came?

Edit: Thanks for clarification