Multi is a term used to refer to accounts other than a player's main account. Though the Policies of Loathing do not state that Multis are not allowed in the game, it does state that Multi abuse is not allowed.
Multis are used for many things, including farming, having other class skills immediately available (not as useful in the post-ascension world), and to let players spend more time using turns.
This is a tricky one. It's not against the rules to have more than one character per household, or per computer, or even per person. What is against the rules, however, is to have a bunch of extra characters that act as item or Meat farmers for your main character.
Here's a yardstick: If your main character is advancing at a rate faster than would be possible without multis, then you're more than likely in violation of this rule.
If you're abusing multis, and your behavior is noticed, all accounts other than what appears to be your primary will be disabled. If you make a bunch more multis and start doing it again, your primary will be disabled.
Examples of abuse are farming, killing monsters in the same dungeon (like Hobopolis), separately buying limited items in the mall, and lending items that weren't donated for. Grey areas are buying things from each others store and donating meat or items to the same clan. Okay things are playing multiple characters that don't interact and using a mall multi.
In the past, advertising budgets for Mall Stores were determined by a store's sales in a given week (which could be supplemented with explicit advertising meat payments). This became a standard method of multi abuse, however, as players would use multis to purchase from their stores and immediately send the purchased items back to their main accounts. For this reason, Jick changed advertising to be explicit payment only. (See the related history entry.)
Many of the hardcore and ronin rules were explicitly created to prevent multi abuse.
Multi Abuse complaints and problems are dealt with by Multi Czar.
Multi Use can be a hard thing to accomplish fairly. It is a fine line between use and abuse when it comes to multis in KoL, and definitions of the line change from player to player, mod to mod, and dev to dev. Many users today are fine examples of Multi Use, from mall multis for HC chars, to HC multis for people who play the market, to extra accounts for the fun of a different approach or more adventures. Just keep in mind this is an adult game and all rules assume you'll act like one.
A mall multi is a secondary character maintained for the sole purpose of conducting mall transactions while a primary character is in ronin/hardcore/bad moon. The restriction on mall multi characters is that they do not provide extra benefit (e.g. meat, items, buffs) for the primary character. Generally this means that mall multi characters should not be using adventures, items, or skills. Provided this restriction is followed, players may then freely exchange meat and items between the primary and the mall multi.
The easiest way to create a mall multi is to adventure until the mall multi reaches level 9 (to purchase a mall store), and then give away that character's meat and items (e.g. via antiraffle). Purists may even find ways to reach level 9 without spending any adventures, usually with the help of stat-gaining items donated from the primary character.
Interestingly, while the main character is in hardcore, it is permitted to lend passive, once-a-day items to a mall multi for the mall multi to use...but there aren't any (of note). Jick is thorough.
Mall multis are mostly useless since players in Ronin and Hardcore can now buy items from the mall. Pretty much their only use is for using the trade system with items in Hagnk's. A niche case could also be for sending outdated items to someone who is Trendy or Slow and Steady.