That will simply expose the function from the scope of functionone, to be a property of the $ object.
For example:
$.functionone = function(){
function setOptions(newOptions){
//...
}
this.setOptions = setOptions;
};
typeof $.setOptions; // "undefined", it doesn't exist
$.functionone();
typeof $.setOptions; // "function"
The this value on JavaScript is set implicitly when you make a function call.
If the function is bound as a property of an object (like $.functionone), the this value will refer to the base object ($ in your example).
That's not so useful IMO, it's equivalent to:
$.functionone = function(){
this.setOptions = function (newOptions) {
//...
};
};
Which is at the end, when you invoke functionone, equivalent to:
$.setOptions = function (newOptions) {
//..
};
The difference is that the function is not named, which can be useful for debugging.
Working with the this value on jQuery plugins is more usual when you extend the jQuery.fn object, in that case the this value refers to the jQuery object that contains the matched elements, and not to the jQuery constructor itself.