Save to Facebook is an addition to Facebook's save feature which allows users of the site to save content they encounter on the web to the "save" section of their Facebook account.
Saving has been included on Facebook for a couple of years and it comes as a surprise that the feature is used by more than 250 million users despite the fact that it is hidden from plain sight.
To use the feature on Facebook, you need to click on the small down arrow icon next to posts made to your Facebook stream, and select the save option from the menu that opens up.
The save text is different depending on the type of content, you may encounter save link or save video for instance on Facebook directly.
Save To Facebook
You control all saved items on the saved page on Facebook: https://www.facebook.com/saved
It lists the most recent saves by default and provides you with a filter list at the top to filter items by type. Next to links and videos, you find photos, places, music, events, or products there as well.
All items are listed with a title, short description, and where they have been saved from. Depending on type, you may interact with it directly, e.g. watch a video you saved that is hosted on YouTube, or are taken to the site instead in case of a link.
Save To Facebook, announced during Facebook's F8 developer conference, is a new option for web publishers to get their content saved and shared by Facebook users.
Basically, what Facebook revealed during the conference is a new button (or text link), that publishers can add to their sites to get Facebook users to save their content on the social networking site.
This sounds like Pocket, Instapaper, or other services that let you do the same, and it is to a degree as you can access some content directly on Facebook's site but not all of it. If you save a video, you may watch it right away if it is hosted on YouTube for instance but links are just that.
Saved articles can be shared easily on Facbeook however, and that is probably the main incentive for web publishers to implement it even though a regular button would do the same.
Only select sites such as Product Hunt have enabled the "save to Facebook" functionality currently as they were part of the beta program.
It is likely however that other sites will join them in the near future, and that plugins for popular blogging platforms such as WordPress will be created as well.
For now, there is an unofficial extension for Google Chrome that you can install to get the functionality for all sites you encounter while using the browser. I could not get it to work during a test run though, and since it requires massive privileges (read and change all your data on the websites you visit), it is something you may want to be cautious about anyway.