In editing mode, you will be able to edit the document directly meaning that any changes you make are automatically added to the document. (Reminder: You can still view edits from other people in the revision history...under the File menu)
In Suggesting mode, any edits become suggestions and are listed out to the right of the document as an option to update the document. When you make a "suggestion", the student can then press the check mark to accept the change or the x to clear the change and not use it. If they accept it by pressing the check mark, the change will automatically be inserted into the document. (See the image below)
To make a suggestion, just make sure you're in suggestion mode and start typing or changing the document as you normally would. You'll see it will highlight the suggested area for changing and keep the former typing in case the student doesn't want to make the changes you suggest. (See the image below)
This is a great tool to be used in conjunction with Google Classroom and a fantastic option for grading papers within Google Drive.