Big minions are minions who have a large chunk of Health and Attack. What qualifies for a big minion is usually a minion around 6/6 which require more than just a standard minion to deal with. Big minions can also be hard to kill without sacrificing minions and cards. The best way to deal with big minions without too many sacrifices is removal and there are plenty to choose from.
Big minions aren't necessarily good or bad, but can overwhelm you the longer they stay on the board.
This is a list of Big Minions:
Legacy[]
Curse of Naxxramas[]
Goblins vs Gnomes[]
Blackrock Mountain[]
The Grand Tournament[]