Trash mobs refers to normal or "white" monsters; not bosses or Elites, that basically serve as cannon fodder in Diablo 3, dying very quickly to any well-geared character. These types of enemies are seldom a danger and in fact are often an aid, allowing characters to generate resource or life by beating on them.
Mobs is an acronym. It stands for "monster or boss" and has come to be used as a general noun to refer to any type of enemy creature. Hence "trash" mobs are weak, worthless, "trashy" or "junky" enemies.
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