Breaking down this function - php

Question

I am using this function for pagination in my site and I am trying to figure it out.
Why are the variables $pages and $ranger assigning values in the parameter field? Why not just set them inside the function?
Also, how is the page adding &paged=(page#) to the URL?
If someone could help me break down this function it would be greatly appreciated. I want to eventually just have a next and previous link instead off all the numbers that are generate so I want to minimzie this function.
here is the function
<?php
function kriesi_pagination($pages = '', $range = 2) {
$showitems = ($range * 2)+1;
global $paged;
if(empty($paged)) $paged = 1;
if($pages == '')
{
global $wp_query;
$pages = $wp_query->max_num_pages;
if(!$pages)
{
$pages = 1;
}
}
if(1 != $pages)
{
echo "<div class='pagination'>";
if($paged > 2 && $paged > $range+1 && $showitems < $pages) echo "<a href='".get_pagenum_link(1)."'>«</a>";
if($paged > 1 && $showitems < $pages) echo "<a href='".get_pagenum_link($paged - 1)."'>‹</a>";
for ($i=1; $i <= $pages; $i++)
{
if (1 != $pages &&( !($i >= $paged+$range+1 || $i <= $paged-$range-1) || $pages <= $showitems ))
{
echo ($paged == $i)? "<span class='current'>".$i."</span>":"<a href='".get_pagenum_link($i)."' class='inactive' >".$i."</a>";
}
}
if ($paged < $pages && $showitems < $pages) echo "<a href='".get_pagenum_link($paged + 1)."'>›</a>";
if ($paged < $pages-1 && $paged+$range-1 < $pages && $showitems < $pages) echo "<a href='".get_pagenum_link($pages)."'>»</a>";
echo "</div>\n";
}
}

Answer 1

The $pages = '', $rage = 2 in the parameter list is defining default values for those arguments, thereby making them optional. In this way, if you call kriesi_pagination() without arguments, it is the same as calling it with the values shown.
The page ID being added to the links is most likely done with the get_pagenum_link() function, which you have not shown here.