How do we define a linearly separable problem? When we talk about Perceptrons, we say that they are limited for approximating functions that are linearly separable, while Neural Networks that use non-linear transformations are not.

I am having trouble understanding this idea of linear separability. Specifically, does it apply only for binary classification or it generalizes for N classes? If so, how does a linear decision boundary for lets say 4 classes even look like?
1.) Perceptron is a non-linear transformation!
2.) Linear seperable function is only defined for boolean functions, see Wikipedia.
Therefore, yes, the statement is meant only for binary classification.
3.) For general functions, see the universal approximation theorem.