A trivial (but very important) example of consistency in an interface is to always pass the same parameters in the same order and, as far as possible, match the order to any relevant prior art.

For example: if your API provides a number of move and copy related elements, you might ensure that they are all (target, source, length).

To the extent that an API is consistent in the way it manages parameters, conceptual units, data structures and so on the API is consistent. 'Orthogonal' is often used and is a related concept.