Visiting i.ytimg.com redirects you to a secure https:// version of the url before giving you an unable to connect error.
Being a typical geek, rather than letting the matter lie I decided to find out what the message relates to. As it turns out the ytimg.com domain is owned by YouTube and I was playing a YouTube video at the time.
Apparently this server is used to serve thumbnail images into the YouTube player (YouTube IMaGe server).
Another mystery solved.
Maybe I can make a conspiracy theory out of it? How about this: YouTube is sending subliminal messages via our browsers? Or this one: YouTube is run by aliens who are tracking our browsing habits to learn more about humanity before taking over the planet?
Can you come up with something more outlandish?
If you are receiving the error "Reading i.ytimg.com" but some web pages aren't loading or YouTube videos won't play, then you will need to check your script blocking software (such as NoScript for FireFox) or anti-virus software (like Kapersky AntiVirus) and enable access to i.ytimg.com. Pages relying on it should then load and you'll be able to play your YouTube videos again.
Youtube has a number of servers that pass various components into its player, so as well as i.ytimg.com you may see messages relating to s.ytimg.com (and possibly others too). An anonymous reader has posted the following link which returns the graphical "skin" for the youtube player as served by s.ytimg.com:
Another example image here, this time the "upload from mobile" icon:
It isn't just images either (at least not from s.ytimg.com):
As has been pointed out in the comments, the "read i.ytimg.com" and "read s.ytimg.com" messages are purely a FireFox issue, but the non-working youtube video caused by anti-virus or adblocking software blocking these sites will affect other browsers too.
John has pointed out that Google own the ytimg.com domain. The explanation for that below:
Link to original press release
Ishino has let us know that Google's anti-phishing API also uses ytimg.com. See http://code.google.com/apis/safebrowsing/ for more details on this.
This is used by Google's HTTPFox Firefox plugin to avoid phishing sites, so you may start seeing messages such as GET http://s.ytimg.com/safebrowsing/rd/goog-malware-shavar_s_(number) or
GET http://s.ytimg.com/safebrowsing/rd/goog-phish-shavar_s_(number) presumably as it is checking the links with Google.