The get method is used to access the DOM elements within a jQuery object:

var allDivs = $(div).get();

In that example, allDivs will be an array containing all the matched elements (in this case, it would contain every div element in the DOM).

The index method returns an integer that tells you the position of the selected element relative to its siblings. Consider the following HTML:

<ul>

    <li>1</li>

    <li id=second>2</li>

    <li>3</li>

</ul>

And the following jQuery:

console.log($(#second).index()) //Prints 1

As for your other question, a DOM node is pretty much anything in the DOM. Elements are types of nodes (type 1). You also have, for example, text nodes (type 3). An element is pretty much any tag.

To make that clearer, consider the following HTML:

<div id=example>

    Some text

    <div>Another div</div>

    <!--A comment-->

</div>

And the following JS:

var div = $(#example).get(0);

for(var i = 0; i < div.childNodes.length; i++) {

   console.log(div.childNodes[i].nodeType);   

}

That will print out:

3 - Text node (Some text)

1 - Element node (div)

3 - Text node (Another div)

8 - Comment node (<!-- -->)

3 - Text node (A comment)

You can find a list of node types here. For an excellent introduction to what the DOM actually is, see this MDN article