Technically, form handler classes are not required as all code can be added directly to a form. The problem with this is that, as form logic gets more logic, it becomes harder to read as the purpose of each method becomes less obvious and less easy to maintain as the amount of code increases. Code placed directly on a form is usually much harder to use by third parties and the code is not reusable.
For this reason, we would usually create a form handler class to handle user interface logic on order entry style forms. These forms usually need a create form in order to make order creation easier. The form handler will act as a way to pass data between the main order entry form and the create form.
Form handlers were used to handle number sequences, but the pattern has changed now as number sequence handling is more logically handled on the form, or...
