Here's how I look at most of the terms used in and around Hearthstone.
Value - A general term that describes a card or play that requires more resources spent to by the opponent to remove it than it does for you to play it. This can refer to mana cost, number of cards, or other game mechanics.
Dr. Boom is an example of value. He often requires multiple cards or more than 7 mana to be completely removed from the game.
Aggressive - A general term that describes minions or decks that are offensively themed and often ignore the board state in favor of directly attacking the opponents hero.
Flame Imp is an example of an aggressive card. You sacrifice your own health in the hope of killing your opponent before it matter.
Tempo - A general term that describes the current minions in play. A player who is ahead in tempo will usually have the only minions on the board or have the largest minions on the board.
Card Advantage - Having more choices on what to play or do than your opponent. This is usually represented by having more cards in hand than the opponent.
Stabilize - A term used to describe a Tempo swing against an aggressive deck.
Aggro Deck - Decks with a low mana curve that want to win the game before turn 10. Examples of this type of deck include:
Face Hunter - Plays cheap charge minions that direction attack face.
Shockadin. - Plays lots of divine shield minions that trade favorably and then attack face.
Tempo Deck - Decks that are very good at swinging the board state in their favor over one or two turns. Examples of this type of deck include:
Spell Mage - Uses cheap spells and spell synergy minions to clear the opponents board while building up theirs. Secrets like mirror entity may also stop the opponent from playing their best minion.
Oil Rogue - Uses removal spells and weapons to kill enemy minions until they can combo a board clear, allowing their minions to trade favorably or attack the opponent for the rest of the game.
Combo Deck - Decks that are dependent on several cards being played in the same turn to win. The synergy from these cards being played together is often enough to swing tempo into your favor. These decks are usually built with lots of card draw mechanics so you can more reliably draw into your combo.
Patron Warrior - Uses spells that damages their minions and grant them charge to kill in one or two turns.
Oil Rogue - Uses weapon buffs and Blade Flurry to clear the opponents board and deal face damage.
Mid-Range Deck - Decks built to Stabilize against aggressive decks and out value them in the late game.
Mid-Range Paladin - Value minions and weapons are used in the early game to trade with the opponent's more aggressive minions and uses high cost value minions to win the match.
Buff Priest - Uses Deathlord and buff spells to slow down aggressive decks, then heals up and uses value minions to win the game.
Control Deck - Decks that rely on Value and Card Advantage to win. Their reliance on high cost, value minions often leaves them vulnerable to fast aggressive play.
Handlock - Uses hero power to draw cards and plays minions that gain advantages while holding lots of cards. Those minions and the diverse options in their hand is how they win games.
Wallet Warrior - Uses weapons and Armor to stay alive into the late game, where the deck uses high cost legendary cards to out value the opponent.
Boorlum - A Card used to damage face and generate value by forcing your opponent to make poor trades against it. Can also be used for reach to finish off your opponent.
Edit:
That took so long to write the conversation moved on