[api] What does "to stub" mean in programming?

This phrase is almost certainly an analogy with a phase in house construction — "stubbing out" plumbing. During construction, while the walls are still open, the rough plumbing is put in. This is necessary for the construction to continue. Then, when everything around it is ready enough, one comes back and adds faucets and toilets and the actual end-product stuff. (See for example How to Install a Plumbing Stub-Out.)

When you "stub out" a function in programming, you build enough of it to work around (for testing or for writing other code). Then, you come back later and replace it with the full implementation.