HTML forms allow users to input data into websites through various input fields like text boxes, checkboxes, dropdown menus, and buttons. Form handling in PHP involves capturing this user input on the server-side. It typically involves retrieving the submitted data, validating it, and processing it further, such as saving to a database. The GET method is generally less secure than POST as it appends data to the URL, while POST sends data in the request body and is not visible in the URL. Form processing refers to the actions taken with submitted form data, like validation and storage in a database.