Mozilla added multi-process support to Nightly versions of Firefox back in 2009. Then in 2011, it made the decision to put development of Electrolysis E10 on ice as other improvements promised to yield a faster return for the browser's user base.
Then back in April 2013 it revived the multi-process architecture feature again and has been working on it ever since.
The main goal of the project is to separate plug-ins, the browser interface and tabs in separate processes to improve the browser's stability, security and performance.
To a lesser degree, it is also something that Firefox lacks that other browser's such as Chrome or Internet Explorer support. Sandboxing on the other hand, something that the new architecture makes possible, is not part of the project but of a related project instead.
A development version of Firefox's multi-process architecture has been integrated into Nightly versions of the browser for some time. It is deactivated by default and needs to be enabled on the about:config page of the browser before it becomes available.
Up until now, you had to set the parameter browser.tabs.remote to true to enable E10 in Firefox. This changes in future Nightly versions as the preference is set to true all the time.
This does not mean that the multi-process architecture is enabled right away though. Mozilla has added an option to the file menu to launch a new OOP (out-of-process) window so that Nightly users can test the feature without enabling it for the whole browser.
The new window makes use of Firefox's multi-process architecture. You will notice that all tabs are underlined in it which indicates that the tab runs in its own process.
Side note: it is not clear if the File menu is the best location for the feature, considering that the menu bar of the browser is not displayed by default. This means that it is likely that many users overlook the new option.
A second switch has been added by Mozilla that will enable Electrolysis by default though, so that all browser windows and tabs make use of it.
The preference browser.tabs.remote.autostart is set to false by default, which means it is disabled. If you enable it by setting it to true, it will enable Electrolysis for the browser.
It is highly recommended to test the feature in its current state using a new profile and not an existing one. You will encounter bugs while you use it. The browser chrome blanked out for instance during my tests. While I managed to overcome this by maximizing the browser window, or minimizing and then maximizing it, it is clearly not suitable yet for day to day work. (via Sören)