A custom field is a textual field that you create, and that is associated with a donor or with a lead.
You can create an unlimited number of custom fields through the My Custom Fields page in your account. Just enter the name of the field and it'll appear in the list of your custom fields. Click the pencil icon to edit the custom field, and the trash icon to delete it.
Once you've created a custom field, it will appear on the profile pages of all of your leads and donors: