As per Drupal's definition "A hook is a PHP function that is named foo_bar(), where "foo" is the name of the module (whose filename is thus foo.module) and "bar" is the name of the hook. Each hook has a defined set of parameters and a specified result type."

hook_theme is one of the most important hook in Drupal and basic purpose of this is to theme output. hook_theme basically returns HTML or it can also specify how a particular render array is to be rendered as HTML.

hook_theme can be used in template.php or in any module file.

In template.php it can be used to theme the theme's template like header.tpl.php. For example:

function mytheme_theme($existing, $type, $theme, $path){
    return array(
        'mytheme_header' => array(
            'template' => 'header',
            'path' => $path . '/templates',
            'type' => 'theme',
            'variables' => array(
                'title' => NULL,
                'some_text' => NULL,
            ),
        ),
    );
}

In module file, we can assign html template for any page. For example:

/*
 * Returns custom content to Drupal
 */
function my_page_function() {
    // Call theme() function, so that Drupal includes the custom-page.tpl.php template
    return theme('my_custom_template');
}

/*
 * Implement hook_theme().
 */
function custom_example_theme(){
    return array(
        'my_custom_template' => array(
            // file name will be custom-page.tpl.php
            'template' => 'custom-page',
        ),
    );
}

I hope this will help someone.