Another cookie option for the masses
Historically Firefox has in some instances stood out as a privacy aware browser, long time users might recall the "block unwanted images" option back in an early version (long gone since then). Why that happened still remains a mystery, but given the impact on ads a conclusion is easy to assume.
With the latest incarnation of Firefox 22 users are offered the possibility to accept cookies from sites they have visited previously when cookies from such sites are sent while visiting other sites, which is if the visitor has cookie favorable settings in their Firefox browser.
The new 3rd party cookie option
An example of the use of the new cookie handling option is when cookies from Facebook are sent as a visitor accesses his Facebook pages, then next or at a later point visits a news site which is riddled with "likes" buttons from Facebook.
Any service on the web can with this setting be ensured of a continued data stream as their visitors hit other sites, and compared to the setting for completely blocking 3rd party cookies as in the Safari browser this appears as a step forward.
The downside is that before the visitor has hit a specific site that sends cookies to others, all of the specific sites cookies will be blocked until the initial visit has occured.
Facebook and others will benefit
Sites such as Facebook and any other like Google that provides features for sites to embed will benefit greatly from this new setting, which might be why it was introduced in the first place.
If you as a user still use Facebook etc then this setting is very likely what you need to select, but before happily selecting it consider if you really need Facebook to track you across the internet. If you can't find a solid reason then the obvious choice it the "never" selection is what you should go for.
Web analytics and ad serving impact
This new Firefox "from visited" setting will have literally no impact or benefit for web analytics or ad serving solutions. If any such solution sends out 3rd party cookies they will have them blocked anyway as it would be very rarely that a visitor had browsed the domain of the data collection or ad serving. In fact it is of no use at all.
Additionally for Google Analytics, which doesn't even send a proper cookie, this is a non issue. The Google Analytics cookie has nothing to do with a 3rd party domain, this despite being measured by one, as it masquerades itself as a 1st party using the domain of the URL in the browser.A bit more secure surfing
If secure surfing with less cookies is your goal then you should seriously consider using a Privoxy proxy server together with Firefox spiced with Adblock Plus and NoScript. Messing around with the "from visited" setting is futile...