A "form" is a document with blank lines or boxes that you write information into. Forms were originally printed on paper, but now forms are common on the Internet. You can see them whenever you sign up for a new website and have to enter your name, email address, and other information.
To "fill out" a form means to write answers into the blank lines or boxes.
Here are some words that you can use after "fill out":
fill out an application
fill out paperwork
fill out a registration form
fill out a survey