Ronery is the 4chan equivalent of the word "lonely", i.e. feelings of friendlessness, social abandonment or isolation that many 4chan users experience.
The misspelling of the word with an "R" is done to mimic the way a person with a thick Japanese accent would pronounce the word "lonely" (a Japanese accent often causes L's to be pronounced as R's, due to the mechanics of many Eastern languages). Its rise to prominence was caused by the movie Team America: World Police and the song I'm so Ronery.
The statement so ronery ;_; or SO RONERY! often comes as a reply to images of Japanese men with hug pillows, advertisements for sex products for lonely men, or other things that indicate loneliness.
Though all boards across 4chan have users that feel lonesome, /v/ and /a/ users are known to be particularly ronery, with ronery threads popping up on said boards from time to time, the sole purpose of which is to communally dwell upon feelings of social isolation the users have. These threads usually contain the question "Anonymous, what's it like to hold a woman in your arms?". Some /v/irgins or /a/ssholes step up and attempt to answer this question, claiming they've actually hugged a girl before, while other users sit back and long to one day feel the feeling these people describe. Some Anonymous denounce or simply ignore these threads, claiming them to be puerile vortexes of self-pity. Other Anons get so emotionally involved in such threads that they claim to actually get moved to the point of tears.
Even when surrounded by friends, it is still completely possible to feel isolated and lonely, so the ronery condition could be said to be something not specific to 4chan, and instead something the majority of normal people actually deal with. Others take a more pessimistic view to the condition, saying that the roneriness seen on 4chan is due to the users' standoffish disposition and geeky, reclusive lifestyle.
Either way, the feeling of being ronery is something everybody can relate to, at one point in their life or another.