I can't make the edits go away

First, don't panic! It's a quick fix. :) Simply go to the Review tab and click the drop-down arrow under "Accept." 

If you want to review and accept changes one-by-one, then click "Accept and Move to Next." If you'd like to accept all of your editor's changes at once, click “Accept all changes and stop tracking":

All insertions, deletions, and in-line changes will be permanent after that, and the red line will disappear from the left side of your document. (You can also go through each change one by one by using the "Accept and Move to Next" option seen above.) 

After you have read through your editor’s comments and made any suggested changes you want to make, you can delete the comments by clicking the first one and going to the Comments section of the Review pane. You can delete the comments individually or all at once:Save your document, and you’ll be tracked-change-free!

For more information, watch this short video.