The Jquery plugin "ajaxForm" is not used to create PHP Form that you mentioned.
ajaxForm is supposed to be used with a PHP Form that is already created. If you have access to the HTML page that submits a form to a PHP script, then ajaxForm allows you to use AJAX (Asynchronous Javascript and XML, or a design method using javascript to make user feedback more intuitive and responsive) with Jquery to handle the events of a form.
Here's a simple use-case:
Before ajaxForm, I have form.html, a document with an HTML form that allows the user to enter their user information to register for my excellent website. Right now they fill the information out, then hit "submit". The form takes this data and sends it to whatever PHP file I designate, the PHP processes this input however I need it to, and then shows the user the next page they need to see (forwards them to say, success.html, which tells them they've successfully registered). This involves a page reload, and if the user uses the back button, they may lose the data they've typed into the form.
Using ajaxForm, you still use the EXACT same form, except by inserting jQuery utiliziing ajaxForm() the Javascript allows the form data to be submitted (possibly some client-side error-detection), but stops any page forwards. The data is submitted, but then it is up to you to define what happens next.
In my original example, user submits the request, but after the request is submitted the PHP would just redirect the user to the same page, just with one more or one less item. So, I use ajaxForm, and then once the data is sent, I re-load the changing portion of the page. Result: user gets instant gratification of their actions, use less bandwidth (portion of page reloads instead of entire page), and they don't lose any of the information they entered into the page.