How does the Hobgoblin buff work?

Let me clear up the first part - "playing" means to have the card come from your hand. Hero powers, while some produce minions (Paladin/Shaman/etc), that is not considered "playing a minion".

If you have multiple of the same card (like the Hobgoblin) the bonuses do stack, which makes that a very formidable tactic. I do the same with the Priest class and the healing powers -- the Northshire Cleric card, it's a 1 att/3 health minion that every time a minion is healed, I draw a card. If I have 3 of them down, I get 3 cards every time I heal. I notice that good opponents tend to take those cards out first whenever possible because of those benefits.

Buffs definitely stack, although some occur one-time (ie Battlecry) and are permanent, but others are "while this minion is active". I've not had this card yet, so I'm not exactly sure which one it is, but it could definitely change the tide of the match if you have several down and are able to play other minions afterward.

According to the Hearthstone wiki, the Hobgoblin only affects minions played from the hand, but two Hobgoblin buffs do stack. That means a 1/3 Voidwalker will become a 5/7. The buff also applies before other enchantment effects, so if you have a Dire Wolf Alpha, the 1-attack minions that you play will still receive the buff.

Hobgoblin's buff will only apply to minion cards--that is, cards which are themselves minions. This is what's meant by "when you play a minion". The buff will not affect minions summoned in any other way, including hero powers (Paladin and Shaman), spell cards (Ball of Spiders, Muster for Battle), or minions summoned by other minions (Violet Teacher).

If you have two Hobgoblins on the board, the buff will apply twice. This makes sense, because all the card asks is whether you summoned a minion with 1 attack--and you did. Even if you also trigger a Sword of Justice or there is a Raid Leader on your board, Hobgoblin should still trigger for the same reason: regardless of what the minion's attack is when Hobgoblin's effect gets to resolve, the minion card itself has 1 attack.

Source: Hearthstone Wiki