While the stats of Poison minions are not always especially powerful, they offer a unique tactical advantage. Poisonous minions can destroy any opponent in a single strike, and can be used to single-handedly dispose of giants such as Ysera or even Deathwing.
Poison minions are generally disposable, intended for a single swift strike. However, abilities such as Divine Shield can allow you to make more extended use of them.
Conversely, note that Poison minions only destroy minions to whom they have caused damage. Minions shielded with Divine Shield will not actually take damage, and will not therefore be destroyed. Reducing a Poison minion's Attack to 0 through means such as Shrinkmeister will likewise prevent the Poison effect from occurring.
Opponents will generally want to destroy Poison minions as quickly as possible, especially if they already have a powerful minion on the battlefield. The presence of a Poison minion, especially a Stealthed one, is a great deterrent to summoning any valuable minions, since they will likely be immediately removed from play.
Betrayal can be especially effective when used on a Poison minion; any adjacent minion without Divine Shield will be killed by the Poison effect.
Poison is actually a triggered effect, but does not display the lightning-bolt icon found on all other triggered effects. However, when the Poison minion deals damage, the lightning bolt icon is revealed.
'Poison' is itself not a keyword (such as 'Taunt' or 'Charge'), but is visually displayed upon minions with a unique animated icon. The case of the Poison ability was cited by Ben Brode as an example where the developers could have added a keyword, but chose instead to simply describe the ability inhttp://hearthstone.huiji.wiki/wiki/Special:RecentChanges full, since it is currently only found on 4 cards.
Keywords were specifically designed by the developers to help players to quickly recognise when several minions have exactly the same ability, such as minions with Taunt, saving time spent reading each individual card's text. However, while keywords make it easier in cases where they are frequently encountered, when such examples are rare, keywords can actually serve to make understanding cards harder, requiring players to mouse over cards in understand to examine their abilities.