Alt is short for "alternate" and refers to a secondary or other character on a player's account.
Having an "Alt" assumes that a player has a "main," a character that they play most of the time. This is not true for all players; some people play numerous characters, none of them especially more than others, though with Diablo 3's long grind to reach high Paragon levels and to accumulate top quality equipment, most players do end up specializing and spending much/most of their time building up one character.
Alts are common in MMORPGs like World of Warcraft, where maintaining one character is a huge time investment and it's very difficult to keep up two. More casual or quick-leveling RPGs lend themselves better to players switching characters regularly, rather than specializing in just one.
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