Using the adjective generalized with algorithms, routines, or functions is obscure. The more appropriate term is generic.
Generics began with early loaders, before full fledged operating systems were developed. The idea was that a module could be loaded into computer memory and the loader was able to perform its function whether the information being loaded was a program, a routine called from a program, an update of the loader, or data to be used by a program. This abstraction was mostly the brainchild of mathematicians such as Kurt Gödel and John von Neumann, both of whom contributed to the same kind of generic representations in the field of abstract algebra.
The ideas of generics spread to the development of file systems. When LISP was developed, the deliberate blurring of the distinction between programs and data was built into the low level functions for working with both. Functional programming developed into higher levels of abstraction in the LISP community.
The idea of generics was introduced into C++ by James Coplien using the term idiom to solve maintainability and readability issues with early clumsy attempt at generic programming using the C pre-prossessing directives. The first highly usable form of generics appeared in Alexander Alexandrovich Stepanov's standard templates library (STL), developed at SGI. Frameworks like COBRA and DCOM were designed to permit generic messaging.
Generic programming constructs spread to Java and then to other languages. Many algorithms are written generically, such that the actual object types with which the algorithm works are not known until the template is employed at compile time.
The multilayer perceptron is a generic learning component, parameterized by a specific numerical representation for forward signal propagation, numerical representation for backward corrective signalling, layer depth, widths and activation functions for each layer, learning rate, and other hyper-parameters. (What are called network parameters are not parameters of the generic network but parameters of that control the mix of inputs into each layer and become the primary data output of the learning process.)
The other artificial network types are similar in this respect.
Even the cell types can be a type parameter in a network. See Neural Network Cell (Node) Types.
The question, "What does it mean when it is said that Machine Learning algorithm results can be generalized?" cannot be intelligently answered. Generalizing results is too general a description of what can be done to results to mean anything. It may just be rhetorical.
There are no universally, "good source[s] for this type of thing." There are many excellent sources for very specific things buried within a hundred times the volume of marginally correct and educationally barren sources. If you don't have the time to scrutinize what you are reading to carefully extract the gems, then it might be wise to attend some courses at a well respected university to get a more solid foundation from a more reliable source than the Internet.