Back in the '80s and early '90s, few people could access The Internet, even if they'd somehow heard of it and wanted to access it in the first place. One of the few groups that could was college students: universities were among the very first Internet adopters, and college-affiliated people, especially students, were one of the main demographic groups on the Internet through the first half of The '90s. The few commercial ISPs that emerged largely catered to a technically sophisticated clientele who were already familiar with UNIX and internet concepts, particularly graduating students who didn't want to lose access to the network as they entered the workforce.
The upshot was that every September, there would be a large influx of new users: college students accessing the Internet for the first time. These newbies were not privy to the manners and folkways of Internet discussion, let alone the technical side of it. Established netizens took it upon themselves to teach the n00bs the netiquette, and within a few months the Internet would go back to being a place for sensible and intelligent discussion.note
Then, in 1993, AOL opened up the then-dominant forum of the 'net, Usenet, to every customer, and Usenet was overrun. The social structure that had worked fine to incorporate a relative handful of newcomers was ineffective in a world where the newcomers vastly outnumbered the old guard. Worse, for every newbie that could be civilized or driven off, more and more took their place immediately. This is the Eternal September, the age the Internet now lives in; most of the old guard are gone, vanished, or formed more minor net societies within the larger Internet as a whole.
The concept, if not the name, existed even before widespread deployment of the Internet. In the BBS culture, the time when the boards were invaded by loudmouth snot-nosed kids was around Christmas, when kids often received computers and modems as gifts. These new users were sometimes referred to as "Christmas ruggies" ("ruggies" being slang for "rugrats," i.e., children). Savvy sysops would disable new signups temporarily around this time.
Since the local culture is too overwhelmed to pass on its customs and social structures, what most often happens is that the old society vanishes and chaos reigns for a while until a new society, with its own rules and customs, can form; alternatively, the older members will attempt to isolate themselves from the newer members. This doesn't always work. Comparisons may be drawn to the Twilight of the Old West or urban gentrification.
Although it's often used as a derogatory term, Eternal September wasn't necessarily a bad thing. It's nearly impossible to imagine such things as wikis or YouTube in the pre-1993 environment, even if the technology could have supported them - or to put it another way, you wouldn't be reading this page. In becoming less "elite", the Internet became less insular and more user-friendly. While it's inarguable that there were losses, it would be the height of stupidity to claim nothing was gained.