function not working on click? (jquery/javascript)

When you put a function or variable inside a function its scope is limited to that function, this means that it will be visible only when inside that function.

To solve this, just move the function that is used outside of "ready function" to be visible outside.

$(document).ready(function(){
    // code here
});

function signupSubmit(){
    alert("hello");
}

Or, better yet. Leave Javascript code to Javascript file only, and let the HTML with HTML only.

HTML

<button id="signup-box-button" type="button">sign up</button>

Javascript

$(document).ready(function(){
    $('#signup-box-button').click(function(){
        alert("hello");
    }
});

This is because of scoping in javaScript as explained by Skarllot

Please refer to know how this keyword works with inline event handlers.

You can use the below code snippet

$(document).ready(function(){

     this.signupSubmit = function(){
        alert("hello");
    }

});

Refer JSFIDDLE

By adding this keyword the function will be registered in global scope. And the above solution may pollute the global namespace.

To better understand the above functionality:

Inline event handlers are evaluated in global scope. In your first example, signupSubmit is not defined in global scope, it is defined inside the function you pass to $(document).ready. Hence the inline event handler cannot find the function.

Here is a simplified example:

function ready() {
    function signupSubmit() { }
}

ready();
signupSubmit(); // ReferenceError because signupSubmit is not defined in this scope

Note that there is no reason to put function definitions inside a $(document).ready callback, except for explicitly not putting them in global scope by using this keyword as mentioned in my first example.