In a browser (not in generic javascript), self is a property of the window object that contains the value of the current window. Since all properties of the window object are accessible as global variables, you can refer to just self and it will contain a reference to the current document's window.
Thus, in your code:
var global=ElizaBot.prototype.global=self;
is assigning to both ElizaBot.prototype.global and to the variable global a reference to the current window object.
See here for info on window.self which is also accessible as just self.
FYI, all of these assignments seem superfluous since the current window object is generally accessible in other ways and need not be stored separately.