Help using ShortCodes to style whole chunks of the post

EDIT 2

Multiple unnamed parameters, starting with equals sign.

function postintro_bb_shortcode( $atts ) {
  // remove equals sign from first unnamed param
  if ( isset( $atts[0] ) && strpos( $atts[0], '=' ) !== false ) {
    $atts[0] = substr( $atts[0], 1 );
  }
  // Param array to string
  $intro = is_array( $atts ) ? implode( ' ', $atts ) : '';
  return '<div class="postintro">' . esc_html( $intro ) . '</div>';
}
add_shortcode( 'postintro_bb', 'postintro_bb_shortcode' );

[postintro_bb=Vivamus sit amet turpis ultricies lorem dignissim sollicitudin id in ex]

Unnamed parameter with closing tag

function source_shortcode( $atts, $content = null ) {
  // remove equals sign from first unnamed param
  if ( isset( $atts[0] ) && strpos( $atts[0], '=' ) !== false ) {
    $atts[0] = substr( $atts[0], 1 );
  }
  return '<a href="' . esc_url( $atts[0] ) . '">' . esc_html( $content ) . '</a>';
}
add_shortcode( 'source', 'postintro_b_shortcode' );

[source=”http://www.example.com/”]test[/source]

---

EDIT

Here’s few ways how to define and use custom shortcodes.

Shortcode with closing tag

function postintro_shortcode( $atts , $content = null ) {
  return '<div class="postintro">' . $content . '</div>';
}
add_shortcode( 'postintro', 'postintro_shortcode' );

[postintro]test[/postintro]

Self closing shortcode tag.

Apparently unnamed parameters work too.

function postintro_b_shortcode( $atts ) {
  $intro = ! empty( $atts[0] ) ? $atts[0] : '';
  return '<div class="postintro">' . $intro . '</div>';
}
add_shortcode( 'postintro_b', 'postintro_b_shortcode' );

[postintro_b blahblah]

Self-closing shortcode tag with named parameter.

function postintro_c_shortcode( $atts ) {
  $intro = ! empty( $atts['intro'] ) ? $atts['intro'] : '';
  return '<div class="postintro">' . $intro . '</div>';
}
add_shortcode( 'postintro_c', 'postintro_c_shortcode' );

[postintro_c intro=”afdfds”]

---

Original answer

The shortcode API is freaking out, because your shortcode name has brackets. Change

add_shortcode( '[postintro]', 'postintro_shortcode' );

to

add_shortcode( 'postintro', 'postintro_shortcode' );