An Alt means an alternate account. As players can only play between 5 and 10 ranked games everyday per account (as limited by the 5 hearts given per day, plus one-half of the remaining hearts from the previous day [no more than 10]), a lot of players created alternate accounts to play more games just for fun or for a trophy run. There are also clans of related alts, such as the Consonants and the Pokemon.
Use of limited amount of alternate accounts is allowed on EpicMafia.
Alts were more widely used when there was no technical limit on the number of alts allowed. This was put to an end due to obvious potential (and actual) abuse from users who would maintain large numbers of alts - some had more than 30 and there were probably a few that claimed to have twice that many.
You can register alts on your profile. Currently, you can have up to 4 alts registered. The first alternate account is free; you must pay for the others.
Note that some players may have been able to receive more than one free alt. For example, players that were among the first 3000 or so to join the site have been given multiple free alts.