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 accounts to increase his or her reputation. These sock puppets can be used to upvote the questions and answers for the puppeteer, or to post questions where they accept the puppeteer's answer.
But do note that multiple accounts do 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 has 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.
As an anecdotal example, I have 2 Stack Exchange accounts: A more professional one tied with my Uni email (wont last forever), & a more personal one tied with my permanent main email. At any time I may be logged in (through device/browser cookies) with either one. I may not wish to hassle switching accounts to interact with a post I already entered with the other account. For ex, I might prefer to create an edit with the current account & approve it at a later time on the original account. Is this allowed? Am I also not allowed to upvote my most important contribution (so it stands out)?
Upvoting your own posts for any reason is completely against the rules.
Any interaction whatsoever on posts you have interacted with with another account is, if not obviously forbidden, at least highly questionable.
When it comes to approval of your own edits, I'd say it's not ok. You could argue that it would not be misuse to approve your own edit because you could just have switched account. And while that is true, you could gain reputation and badges for your second account for doing so. And it could possibly be a lot of other factors that I cannot even think about right now. Also, bear in mind that you might get caught by bots while doing this, and resolving such situations would require manual intervention. And it is not really reasonable that the moderators should have to deal with this just because you don't want to switch account. So stay away from your own posts and actions completely.