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A shortcode is a string in square brackets that will be replaced by a callback function.

There are four built-in shortcodes in WordPress: [embed], [wp_caption], [caption] and [gallery].

A shortcode can be registered with:

add_shortcode( 'shortcode_name', 'callback_function' );

The callback must return a string, it must not output anything directly.

Wrong:

function shortcode_callback()
{
    echo 'called';

?>
Hello, I am doing it wrong.
<?php
}

Correct:

function shortcode_callback()
{
    return 'called';
}

The callback function can use three parameters.

Example

A shortcode was used in a post like this:

[sample color="red" tag="div"]Some text.[/sample]

The callback can use the information from this shortcode like this

function shortcode_callback( $args, $content = '', $shortcode_name = '' )
{
    $output = '<' . $args['tag'] . ' style="color:' . $args['color'] . '">' 
        . 'The shortcode ' . $shortcode_name . ' was called.<br>'
        . $content
        . '</' . $args['tag'] . '>';

    return $output;
}

See also the Codex: Shortcode API.