Formal definition of loss surface of multi-layered networks
In the empirical risk minimization framework, we let $w$ denote the weights of the neural network (which we are trying to learn) and define $L(w)$ to be the total loss (across the entire training set) if you use weights $w$.  Then, the optimization problem is to find $w$ that minimizes $L(w)$.

This is the function that the quote is talking about.

"Loss surface" refers to the graph of this function.  $L$ is multidimensional so we obtain a graph in some high-dimensional space.