I found a Meta Stack Overflow post in whose answer Servy says:
it's sock puppeting and is a very serious violation
"Sock puppeting" is a picture. But why a sock? Is it like playing with your own sock?
Simply, a sock-puppet is a puppet which has been created using a sock.
In this context, a sock-puppet is one person pretending to be another. What you see is the puppet but the actions and voice are those of the person controlling the puppet.
On messageboards and websites a sock puppet is the online alter-ego of somebody else.
The most popular definition on Urban Dictionary is also the earliest, from 2003:
Oxford English Dictionary
The OED doesn't have this meaning, but has two earlier meanings that shows the development:
The first hand puppet use is:
The first minion use is:
A similar figurative use can be found in the older term, puppet government, which can be traced back to puppet King used in 1611.
Here's the 1993 in bit.listserv.fnord-l:
Let's delve further into Usenet to see where the fake account meaning comes from.
It was used extensively in rec.gambling.blackjack from September 1996 onwards in hundreds of posts about one person's gambling method and the numerous sock puppets who backed him up. These sock puppets were referred to as separate individuals (December 1996):
But some suggestions were made it was the same person, for example (September 1996):
And in September 1996:
And in September 1997:
By February 1998, sock puppet had both meanings of a minion and of a fake account: here's "Sock puppet defined":
@Ste's answer is correct and should be the one accepted, but I wanted to add that most messageboards and websites forbid sockpuppets and will sometimes terminate not only the sockpuppet but also the original account of the user who created the sockpuppet in the first place, although sockpuppets are not necessarily created for nefarious purposes. A friend of mine created a sockpuppet on a particular message board in order to argue with himself and create a better experience for everyone on the board, or at least that was his stated intent. On the other hand, a guy that was working to defeat me in an "edit war" on an article on Wikipedia created two sockpuppets to create a false sense of consensus around his point of view. He and his sockpuppets got sent to outer darkness once this was discovered.
It can be more subtle. Two or more people can contrive to create individual accounts that are in fact associated with different people, and still be effectively sockpuppeting, if the accounts were created in order to collude towards a common goal. An example in literature can be found in Orson Scott Card's novel Ender's Game, where Andrew "Ender" Wiggins' brother Peter and sister Valentine post what become influential essays of political discourse as "Locke" and "Demosthenes", respectively, in order to influence public policy. They come across as independent anonymous individuals, but are in fact complicit with each other towards a goal, leading eventually to Peter becoming the effective ruler of Earth.