well, the "zine" bit is pretty straight-forwards. it basically implies a small, community-driven, freely-distributed magazine, and the term has a background of use in punk culture as well. "lain" is the tricky bit, then. lain originated in a late 90s "avant-garde" anime series, but, in the two decades since, has grown and evolved into a (sub)cultural icon. lain implies an aesthetic, a mentality, a philosophy: connection and isolation, ubiquity and obscurity, love and terror, trust and paranoia, selflessness and narcissism, and seemingly countless other themes beyond the obvious memes of "old computers and animu" one might discount it as at first glance.
these days, lain appears in bubbles all across "the wired", coming and going but never disappearing completely. in an internet where most content has been absorbed by a few giant corporations and organisations, lain remains decentralised, manifesting in small, isolate communities, one-off art projects, forgotten blog posts and dusty web pages, bad fanfics and over-ambitious projects, and sometimes even apparent cults.
the lainzine itself is a project spawned from the imageboard lainchan, which, along with the other projects that have grown from it, forms what's likely the largest "lain bubble" currently active. lainchan being a western imageboard, the zine also carries themes of "/cyb/" (cyberpunk and its aesthetic) and "alternative culture", along with anything else bound to appear at a crossroads of anime, computers, and anonymity.
well, try reading a bit and find out. past issues can all be found over at the archive. "production quality" varies a bit, as it's taken a while to find the right people for presenting things well and making them pretty, but there're interesting things to read no matter which you pick up.
and, if you like what you see there and have something you want to share as well, please don't hesitate to read the submission guidelines and do so! as a free community project, the lainzine is what people make of it, with those people being anyone at all who feels some sort of affiliation with lain and the many things the name has come to mean. so don't feel like your work or ideas don't belong just because they differ a bit from what's been in past zines. we're all connected, after all :P