Arrays are used in my opinion so that you don't have hundreds of variables and just a few nice arrays so it's used to hold variables. Here is a quick example of code using variables and then code using arrays.
CODE
<script type="text/javascript">
<!--
var monday = Monday;
var tuesday = Tuesday;
var wednesday = Wednesday;
var thursday = Thursday;
var friday = Friday;
var saturday = Saturday;
var sunday = Sunday;
document.write("Todsay is monday");
//-->
</script>
<!--
var monday = Monday;
var tuesday = Tuesday;
var wednesday = Wednesday;
var thursday = Thursday;
var friday = Friday;
var saturday = Saturday;
var sunday = Sunday;
document.write("Todsay is monday");
//-->
</script>
So there we have the variables and the document write, sorry if there are any mistakes as I jotted that up quickly. Here is the array version which is much better.
CODE
<script type="text/javascript">
<!--
var days = new Array("Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday", "Sunday");
document.write("The day is " + days[5] + "!");
//-->
</script>
<!--
var days = new Array("Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday", "Sunday");
document.write("The day is " + days[5] + "!");
//-->
</script>
This will output 'The day is Saturday!' and can be used differently or whatever but the basic rundow is that you define a variable then the equal operator and type new Array(""); I used days of the week so we didn't go too advanced but heres another way to create arrays and this is the way that I first ever learned.
CODE
<script type="text/javascript">
<!--
var days = new Array(3);
days[0] = "Monday";
days[1] = "Tuesday";
days[2] = "Wednesday";
//-->
</script>
<!--
var days = new Array(3);
days[0] = "Monday";
days[1] = "Tuesday";
days[2] = "Wednesday";
//-->
</script>
Although the code is longer it is more easily set out for the beginner to arrays, also you must note that new Array(3); was used as you have [0][1][2] which are the (3) if that made any sense to yeah, anyway I haven't added all the days of the week as that would be really long and I don't have the typing energy. We haven't used arrays for much yet but here is something we could do with the if/else condition but I will save that for another day.
Hopefully I will write a few more javascript tutorials for 13Dots as it's been great