This checkbox is unchecked by default, meaning that they are not mandatory fields.
If a field is mandatory, and the object is saved or submitted with a blank value, the user will be prompted with the message entered into the Validation Message section of the custom field settings.
If the Validation Message is left blank, the text "X can not be empty." will be displayed in a pop-up, where X is the custom field's caption.
The captions of mandatory fields automatically have special formatting applied to them to indicate that the given field is mandatory.