Arcane is a mage-specific keyword. While you have Arcane (either by a minion or a spell), you get a copy of any spell that you cast, but costing 3 more (of the casting cost). Example: you cast Arcane Missiles, you get a copy that costs 4, you play that copy, you get another Arcane Missiles, but this one costs 7 (the casting cost was 4 this time). This way it can't be abused (I guess).
Vibrate is a keyword that activates whenever a Battlecry activates (including if your opponent plays it). So, you could say it's like Inspire, except that the trigger is a Battlecry minion being played. The effect happens after the Battlecry ends, so if you kill a Vibrate minion with a battlecry, the Vibrate effect doesn't go off. Here are some examples:
Scout was already done but ok i come up with mine then. SCOUT: Whenever a minion with SCOUT is played with for example SCOUT 2, you are able to see three cards in your opponent's hand or deck. these cards are picked at random and make clear what the opponent has so you caan play around that and have an idea what your opponent will do.
Ethereal (on a Minion or Weapon) means that whenever the card is destroyed a copy is given to the opponent, sometimes with additional text or effect. Minions with Ethereal will be destroyed if your opponent has a full board, while Weapons with Ethereal will destroy your opponent's weapon if applicable. For example: