Yes, "its" means "the data's interface" in that context.
Another way to look at it is an object is intermediate between data local to a function, and global to the entire program. Sometimes it's convenient for a group of functions to share data, and so those functions and data are grouped into an object. To ensure the consistency of the data, no other functions should have access to it, so the data is private, and all access from other code needs to be through the objects member functions, and that becomes the interface between the data and the rest of the program.
All the regular functions of an object should read or modify the data, or there's no point in putting them in the same object. Static methods are an exception, as they are pure functions where the output is produced only from the input. They should relate to the inputs or outputs of the other functions in some way to make sense, but I wouldn't count them as part of the interface.
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