A Web form is a collection of GUI controls on a page. The user selects options in the controls, and then submits the form to the server. The server performs processing based on the user's selections and returns a resulting page to the user.
Form processing implies that action is taken on the server, and therefore requires server support for one or more server-side programming technologies. Programming ability is normally required.
Forms are made up of standard GUI controls such as checkboxes, text fields, and buttons. The user can operate these controls with the mouse or keyboard in order to 'fill' the form with their data.
User submits form
A form does not normally 'do' anything until the user submits it. The form is initially downloaded from the server as part of the normal HTML page; there is no further communication until the user submits a form.
Forms are submitted to the Web server at a URL given in the <form> tag.
Server processes form
The server is sent form data in one of two ways: either as part of the requested URL (which is appropriate if the amount of data is small), or in additional data sent with the URL request (which is appropriate if the amount of data is larger or if the data could cause some kind of effect, rather than just requesting information).
The Web server generally acts on the request by passing it along to associated software designed to handle it. The software may communicate with a database in order to handle the request. It then returns a resulting page to the user which indicates the result of the action.
If you want your site to handle information from forms, then the server must be able to run software to handle that data. Most free providers do not include support for this, so you will generally have to pay for Web hosting that includes this.
Even if you want to use other people's software out of the box to process your forms, installing server-side software is usually a difficult administration task, and you must be sure that your Web host supports the particular required technologies.
Obviously, developing your own custom software to respond to forms requires programming skill.