My original definition from this writeup: "Finnish expression meaning a 'net cretin. The name is said to come from user name firstname.lastname@example.org." Allow me to explain without extensively quoting other sources...
Typically, "peelo" is used to refer to IRCers who have no manners and are only making fool of themselves. Typically, we're talking about either complete and utter newbies (in which case peeloism is curable), or kids roughly between 10 and 15 (in which case it is also curable, but it needs to wait until these people actually grow a brain, and even then it is not that certain). Peeloism implies general clowning around and disregard for IRC channel rules and etiquette, and/or communication that has nothing worth of communicating (I believe the expression is "waste of bandwidth with inane chatter"). Typically, these people pop on a channel and loudly beg for company (attractive members of opposite sex, typically), call people names (when objecting, disagreeing or, sometimes, agreeing to something they say) - and often not even showing particularly creative insulting skills... and they also get /kicked around like no tomorrow when the channel ops wake up.
These days, IRC peeloism is fortunately getting rarer and rarer, and you may again hear some intelligent discussion if you listen very carefully; most peelos flock on Web-based chatrooms.
"Peeloism" can also be extended to mean general show of ineptitude on computer use (such as building personal homepages that have tons of bells and whistles but are pain to look and have little content - most kid web pages seem to qualify). Or, more rarely, general ineptitude on non-computer things.
I originally heard that the source of the expression was user name email@example.com, but I never heard much more. The story based on recent research suggests something far more grandiose.
Freenet Finland - freenet.hut.fi - was a free text-based Internet access point for children, and became very popular among school kids. Along with E-mail/WWW/Gopher/Usenet access, it also gave IRC access, something the regular IRCers obviously objected to, because the IRC was then flooded with clueless newbies.
Now, Freenet was not only used by kids, but also people who worked in education. In 1995, Pekka Elo was, among other things, member of the Finnish National Board of Education and chairman of the Humanist Union of Finland. And as everyone knows, humanists aren't always very good with computers. He wasn't particularly good at using Freenet's line-based text editor when posting to Usenet newsgroups, for example. Still, his technical problems were generally understood and tolerated there.
Supposedly (no one has a log of this happy occasion), one day he mistakenly picked the IRC from Freenet menus, and managed to fool around before someone finally told him how to exit. Freenet by default assigns the user name as user's nick and joins to #freenet. Naturally, everyone assumed he was one of the countless brainless kids in Freenet, and one may assume he did pretty badly, because quite soon after that, the expression "Peelo" was already being used widely.
See also: Teini-X
Ren. "Peelobongarin opas". Teletappimaa, 19/10/2003. Online. <URL:http://members.vip.fi/~muurinen/peelo.htm>. Accessed 2003-08-17.
Ville Heikkilä. "Mistä peelo-sana todellisuudessa syntyi?". PELU PAKETTI
, 2003. Online. <URL:http://www.pelulamu.net/peelo/>
. Accessed 2003-08-17.