There are a growing number of assignment types available:
This is useful when the assignment is performed outside of Moodle. It could be something elsewhere on the web or face-to-face.
Students can see a description of the assignment, but can't upload files or anything. Grading works normally, and students will get notifications of their grades.
This assignment type asks users to edit a text, using the normal editing tools. Teachers can grade them online, and even add inline comments or changes.
(If you are familiar with older versions of Moodle, this Assignment type does the same thing as the old Journal module used to do.)
Upload a single file
This type of assignment allows each participant to upload a single file, of any type.
This might be a Word processor document, or an image, a zipped web site, or anything you ask them to submit.