Add to Menu provides a quick link in your Joomla! administrator pages to quickly add a menu item link for the article or page that you are viewing. For example, you need to create a new article, add a link to that article in your menu, and then edit the article some more...

With Add to Menu this is done easily and quickly:

Create the article and save it;
Now, whilst still in the article edit page, click on 'Add to Menu';
Select the menu you want to the new menu item to be in;
Click 'Save'.
And voila! You are done.

Without Add to Menu this takes a lot of steps (not even listing all!):

Create the article;
Save and close the article.
Create a new menu item under the correct menu;
Add the menu title;
Select the correct page type;
Find and select the correct article;
Save the menu item;
Go back to the Articles Manager;
Find your article again;
Open your article.