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Whats the meaning of $('element',this.el)[0]?

Now I learning Backbone and Marionette, I read some tutorial and I found a code whom I haven't understand. Here's the code:
$('element',this.el)[0]
I know jQuery little bit. I know this keyword, i know the $('element') keyword, but not understand that code, please everybody tell me about that.

This $('element',this.el) says select all <element> contained within this.el. this.el must be another "object" but what it is depends on what is building this higher up. I cover this in more detail in this answer to a similar question.
The [0] simply unwraps the jquery object returning a vanilla DOM object. So:
$('element',this.el).first(); //works
$('element',this.el)[0].first(); //will error
The second errors becuase it is no longer a jquery object so it is not wrapped in the jquery functions.

In Backbone context, your code is probably found inside a view and this.el refers to the view's element
$('element',this.el) find the element nodes inside the scope defined by this.el
$('element',this.el)[0] refers to the first element node found
Note that in a Backbone view, you can simplify to
this.$('element')[0]

This is the jquery selector context syntax:
'element' is to a selector and this.el is a context and using bracket notation to get the first element [0] which also converts jquery element to javascript object.
Alternatively you can use like this instead of jquery selector context syntax:
$(this.el).find('element')[0] // hope you understand this syntax

Why is JQuery messing with the params I want to bind to a click handler?

In short, I'm doing this:
function myHandler(a,b,c,d){
doStuffWithMyParams(a,b,c,d);
}
Then somewhere else:
jqueryElem.click(myHandler.bind(a,b,c,d));
When I do, some of the parameters passed (a,b) are read correctly. But the third (c) is a JQuery event object. I've also tried binding the args as an array. Then, the first param becomes the event object.
Totally perplexed here. Thanks in advance for any direction on this.

With the code myHandler.bind(a,b,c,d), the argument a is the context that bind() uses
So my handler is actually seeing this
function myHandler(b,c,d,event){
So I have a feeling you want
jqueryElem.click(myHandler.bind(this, a,b,c,d));

Building on what epascarello wrote, this should do the trick:
jqueryElem.click(myHandler.bind(this,[a,b,c,d]));
Not having the array might cause b to be treated as an eventHandler. Notice I used an array, but it could also be an object, for instance.

is there a difference between the jquery code here?

Here is the code block a
$('ul.filter li').each(function() {
$(this).click(function(e) { //do something });
});
Here is code block b
$('ul.filter li').click(function(e) { //do something });
Don't these do the same thing? is one better than the other? Which one is the better/faster method?
I would assume block b since it has less code but I want to confirm it here, thanks

The effect you see will be the same, but in the first case, every li element is assigned a new function, as you are creating the function object inside the each callback.
In the second case, there exists only one copy of the event handler, which means it uses less memory over all (although this is probably not measurable).
Internally, click calls on (in jQuery 1.7), which is iterating over the elements via each as well:
return this.each( function() {
jQuery.event.add( this, types, fn, data, selector );
});
This is the case with many jQuery methods (most often noted in the documentation), so you are saving characters and memory by letting jQuery implicitly do this.

They would both have the same effect.
I would prefer the second only because it is more concise and you're creating a single anonymous function to handle the click rather than an anonymous function per element.

For Jquery philosophy, the second is better because it is shorter.

Both are more or less same and give the same results. The second code snippet will also internally run each loop and assign the click handler to each li element.
But yes the second code snippet is very clear and simple.

The second usage is called "implicit iteration" and is one of the cornerstones of jQuery.
For example, in JavaScript Definitive Guide, 6th Ed, p.530 for jQuery Basics:
Despite the power of the each() method, it is not very commonly used,
since jQuery methods usually iterate implicitly over the set of
matched elements and operate on them all. You typically only need to
use each() if you need to manipulate the matched elements in
different ways. Even then, you may not need to call each(), since a
number of jQuery methods allow you to pass a callback function.
in http://jqfundamentals.com/chapter/jquery-basics
Implicit iteration means that jQuery automatically iterates over all
the elements in a selection when you call a setter method on that
selection. This means that, when you want to do something to all of
the elements in a selection, you don't have to call a setter method on
every item in your selection — you just call the method on the
selection itself, and jQuery iterates over the elements for you.
Typically, when the library has this built-in as the standard way of doing it, it will be in general better and faster, or else they wouldn't have built it in.

jQuery plugin: I would like to be able to access the selector from the method called.

This is a simple example. Here is the call to the method.
$('.className').somePlugin.someMethod(1);
My question is: How do I access $('.className') within the below method?
$.fn.somePlugin.someMethod = function(someNode) {
enter code here
}
I would like to dynamically get the $('.className') object from within the method as illustrated above. Any idea if this is possible without having to do something like this:
$.somePlugin.someMethod('.className', 1);
Thnaks in advance.

I've seen some mumblings about there being a selector attribute on the jQuery object. I've never tried it though. It goes like this...
$(this).selector
Take a look at jQuery end(). It may be of some use to you here.
http://api.jquery.com/end/

Control references in jQuery

function eegetdropdownvalue_str(ctl){return ctl.selectedIndex>=0&&ctl[ctl.selectedIndex]?ctl[ctl.selectedIndex].value:''}
The above function is called with
co.p1A10=eegetdropdownvalue_str(document.formc.p1A10);
I want to switch the call over to jQuery to drop the document.form reference however doing this
co.p1A10=eegetdropdownvalue_str($('p1A10'));
Does not reference the control correctly - How should I do this?

There's two things wrong with your code.
First, $('p1A10') references nothing.
jQuery selectors work almost identically (if not completely identically) to the way css works.
So, just ask yourself how you would reference the object(s) in question in CSS and you're half way there.
I'm assuming that p1A10 is the name or id of an object. Since we're using CSS/jQuery syntax, this should be an id, although you can select by other attributes such as $("select[name='p1A10']") .
To reference an object by ID we use the # character (again, just like in CSS). So we can select your node via $('#p1A10').
The second problem is that your function is expecting a DOM object not a jQuery object. To keep your code intact, we need to say $('#p1A10')[0] where 0 is the first element within the collection of jQuery elements.
I've provided two examples to explain this a little better. One uses your existing infrastructure and one replaces it.
http://jsfiddle.net/TD6Uu/5/
Hope it helps.

Given a form with id formc and a select with name p1A10 you could e.g. use:
o.p1A10 = eegetdropdownvalue_str($('#formc select[name="p1A10"]').get(0));
If this doesn't do it, please provide use with the exact HTML structure