What you've got there is a function expression, not a function statement.
In a function statement, the name is mandatory. In a function expression it is optional. A function expression with a name is called a named function expression. A function expression without is called an anonymous function
There are a number of subtle differences between all these different methods of declaring a function which are covered in this question; var functionName = function() {} vs function functionName() {}
What you're doing here is setting the onopen property of exampleSocket to a function (expression). Note that you are not running that function at all; you are simply declaring it, and saving a reference to it in exampleSocket.onopen.
This means that someone can execute that function when they want to by calling;
exampleSocket.open();
They can pass a parameter to the function, which you can use inside the function using the event variable (and to answer your question; event is not a special word. You can call it anything).
exampleSocket.onopen = function (event) {
console.log(event); // will log "hello"
};
exampleSocket.open("hello");
The fact the variable event isn't used anywhere will likely mean the developer has named the argument to say "hey, look, you can use this if you want to", but hasn't in his actual implementation.
You don't have to declare the variable yourself. It is declared already by being named in the argument list, and it will be initialized to a value when someone passes an argument when they call the function.
Note that we could define this event handler using a function statement;
function foo(event) {
console.log(event);
}
exampleSocket.open = foo;
... or via a named function expression:
exampleSocket.open = function foo(event) {
console.log(event);
};
To confuse things (don't worry about this; it's a quirk of JavaScript) the name of a named function expression is only available inside the function itself;
exampleSocket.open = function foo(event) {
console.log(event);
console.log(typeof foo); // you'll get "function"
};
console.log(typeof foo); // you'll get "undefined"
... but in a function statement, you'll be able to access the name both inside and out.
I hope this helps... it's a bit of a "brain dump" of information :).