The on-site description currently available is the tag-wiki for the tag sock-puppet:
A sock puppet is an extra account created in addition to the user's normal account and used for abusive purposes.
A sock puppet is an extra account created in addition to the user's normal account.
On Stack Exchange, one abusive reason for sock puppetry is serial voting, especially upvoting own answers.
Users found to be abusing sock puppets will have such accounts deleted and their main account will be suspended or deleted.
Note that having more than one account for a legitimate purpose is permitted.
Here at Stack Exchange, it often means someone who creates multiple accounts and uses these extra account to increase his or hers reputation. These sock puppets can be used to upvote the questions and answers for the puppeteer, or to post questions where they accept the puppeteers answer.
But do note that multiple accounts does not necessarily imply sock puppetry. As long as you are not using the extra account for evil deeds, such as vote fraud, you are fine. One commenter to this post have one account that he/she uses on untrusted connections.
A sockpuppet is an online identity used for purposes of deception. The term, a reference to the manipulation of a simple hand puppet made from a sock, originally referred to a false identity assumed by a member of an Internet community who spoke to, or about, themselves while pretending to be another person.
The term now includes other misleading uses of online identities, such as those created to praise, defend or support a person or organization, to manipulate public opinion, or to circumvent a suspension or ban from a website. A significant difference between the use of a pseudonym and the creation of a sockpuppet is that the sockpuppet poses as an independent third-party unaffiliated with the puppeteer. Sockpuppets are unwelcome in many online communities and may be blocked.