Knowing your opponent.

“If you know the enemy and know yourself, you need not fear the result of a hundred battles. If you know yourself but not the enemy, for every victory gained you will also suffer a defeat. If you know neither the enemy nor yourself, you will succumb in every battle.” - Sun Tzu 

There are millions of Hearthstone players across the world, so it would be difficult to get to know each and every player and learn how they play. However, there are only a certain number of decks that are played in any given meta (usually up to 20). Assuming there are 20 decks being played, around 2-3 of them will be Tier 1, which most of the meta is going to be comprised of. Knowing how to play 1 of these Tier 1 decks is enough to climb to legend but knowing how to play against the other Tier 1 decks is key. If you have the time, you also want to know how to play against the Tier 2 decks, but the Tier 2 decks usually play in a similar way as the Tier 1 decks.  
Knowing your opponent’s deck is important for 3 main reasons: threats, direct damage, and removal. 

Having knowledge of your opponent’s deck is key to making the optimal decisions. By understanding what threats the opponent can play, you are able to know when you should play certain removal spells and when they should be saved. 
Let’s look at an in-game situation.  

Threats 
If I am playing Control Paladin versus Imp Warlock and I have a City Tax (2 mana spell that deals 1 damage to all enemy minions) on turn 2 and they have 2 1/1 imps on the board, should I play the City Tax or save it for a bigger board? If I save it, the worst that can happen is for my opponent to play cards with Imp synergy, such as Vile Library (2 mana location that gives a minion +1/+1 for each imp they control) or Impending Catastrophe. If I recognize the Vile Library to be the main tempo-generating threat that I wish to mitigate the effects of, then I should play the City Tax to clear the minions. However, Imp Warlock also plays Fiendish Circle (3 mana spell, summon 4 1/1 imps), and City Tax would be much more valuable and efficient to clear the imps summoned from Fiendish Circle. So, should I play the City Tax or save it for the Fiendish Circle? There’s no single answer to this question. It always depends on the specific situation. For example, if I was holding 2 City Taxes, then I would be more inclined to play one to clear the imps summoned from Wicked Shipment because I have another for the Fiendish Circle. If I only had City Tax as my clear and the rest of my hand was full of minions, I would be more inclined to save it to get maximum value from the card. 

Direct Damage  
Knowing how much direct damage your opponent plays is another key component of winning because it tells you what your “real health” is. What I mean by that is if you have 15 health and your opponent is holding a fireball that they can use whenever they want, how much health do you really have? You have 9 real health. Many players fail to understand this concept and get surprised when they get bursted from a combination of damage from board and hand from their opponent. They rarely pay attention to how many turns their opponent has been holding a certain card for, then when their opponent has a combo that finishes them off, they are surprised.  

For example, if I am against a Rogue, I am aware that most of them play 2 copies Wicked Stab (2 mana spell, deal 2, 4, 6 damage at 1, 5, 10 mana) and 2 copies of Tooth of Nefarian (2 mana spell, deal 3 damage). Throughout the game, if I notice that my opponent has been holding 3 cards and hasn’t played any direct damage spells (Wicked Stab and Tooth of Nefarian), then I will assume that they have up to 11 damage in their hand. This makes my real health whatever it is at the time minus 11 because as long as my opponent has 6 mana, they can deal 11 damage.  

Removal
Knowing what removal cards your opponent plays in their deck is crucial to making optimal decisions. Oftentimes I see beginners constantly maximize their tempo without any care for what the opponent plays in their deck. They will keep throwing out minions onto the board every turn, which is great tempo generation! Then their board gets hit with a board clear and they have no minions on board, and because they spent all their time playing minions onto the board instead of drawing or generating any value, their hand is also empty. This is a result of not knowing what removal cards the opponent was playing. 

Let’s say I have minions with 3/3, 4/3, and a 5/5 stats on the board against a Mage with an empty board heading into turn 7, and I have the choice to play either 1) a 4/5 minion or 2) Arcane Intellect to draw 2 cards. Which one should I play? Playing the 4/5 will make my board even stronger so that I can beat my opponent as fast as possible, whereas Arcane Intellect, while not affecting the tempo, will ensure that I have more cards to play in future turns if anything goes wrong. A player who isn’t aware of what Mages can do on turn 7 would play the 4/5. More tempo! That’s good, right? No, not necessarily, and therefore knowing what removal cards your opponent plays is crucial. If I play the 4/5 minion and my opponent plays Flamestrike, then my tempo would be completely reset and I would lose the 4/5 that I spent my precious mana on. Regardless of whether I played the 4/5 or not, my opponent was likely to play Flamestrike on the board since they were facing a threatening board with no minions to fend them off. In this example, it is better to play the Arcane Intellect, so that when my opponent plays Flamestrike, I still have the 4/5 minion in my hand to play next turn, plus an additional 2 cards that I can play if I like.