In this context, the word "stub" is used in place of "mock", but for the sake of clarity and precision, the author should have used "mock", because "mock" is a sort of stub, but for testing. To avoid further confusion, we need to define what a stub is.
In the general context, a stub is a piece of program (typically a function or an object) that encapsulates the complexity of invoking another program (usually located on another machine, VM, or process - but not always, it can also be a local object). Because the actual program to invoke is usually not located on the same memory space, invoking it requires many operations such as addressing, performing the actual remote invocation, marshalling/serializing the data/arguments to be passed (and same with the potential result), maybe even dealing with authentication/security, and so on. Note that in some contexts, stubs are also called proxies (such as dynamic proxies in Java).
A mock is a very specific and restrictive kind of stub, because a mock is a replacement of another function or object for testing. In practice we often use mocks as local programs (functions or objects) to replace a remote program in the test environment. In any case, the mock may simulate the actual behaviour of the replaced program in a restricted context.
Most famous kinds of stubs are obviously for distributed programming, when needing to invoke remote procedures (RPC) or remote objects (RMI, CORBA). Most distributed programming frameworks/libraries automate the generation of stubs so that you don't have to write them manually. Stubs can be generated from an interface definition, written with IDL for instance (but you can also use any language to define interfaces).
Typically, in RPC, RMI, CORBA, and so on, one distinguishes client-side stubs, which mostly take care of marshaling/serializing the arguments and performing the remote invocation, and server-side stubs, which mostly take care of unmarshaling/deserializing the arguments and actually execute the remote function/method. Obviously, client stubs are located on the client side, while sever stubs (often called skeletons) are located on the server side.
Writing good efficient and generic stubs becomes quite challenging when dealing with object references. Most distributed object frameworks such as RMI and CORBA deal with distributed objects references, but that's something most programmers avoid in REST environments for instance. Typically, in REST environments, JavaScript programmers make simple stub functions to encapsulate the AJAX invocations (object serialization being supported by JSON.parse and JSON.stringify). The Swagger Codegen project provides an extensive support for automatically generating REST stubs in various languages.