BBCode to HTML conversion is usually done on server side thus at least one server request is required to display the result. BBCode2HTML is a JavaScript function implemented to do the conversion on client side so the result can be previewed without hitting the server. Supported BBCode tags and a live preview example can be found at BBCode Editor page.
JsAutoP is the JavaScript equivalent of the PHP function described at Matthew Mullenweg's website. The PHP function is a part of Wordpress code, which is used to convert new lines to HTML line breaks and paragraphs inside user entries. A similar function is also used in Drupal for the same purpose.