Abilities are the rules that will trigger based on events that happen within the game. Although some of them are only present on the cards playable by a specific Hero, they still can be played by any Hero if you manage to accquire them in an ongoing game (e.g. Thoughtsteal).
Battlecry
An ability that is triggered when the minion is first summoned into play.
Charge
This ability means the minion can attack on the same turn that it is summoned.
Choose One
When some condition is met, the controlling player may choose which of a number of effects activates.
Combo
A bonus if you already played a card this turn.
Counter
A card that is Countered has no effect.
Deathrattle
An ability that is triggered when the minion dies.
Divine Shield
The first time this minion takes damage, ignore it.
Enrage
While damaged, this minion has a new power.
Freeze
Frozen characters lose their next attack.
Immune
Cannot be damaged.
Overload
You have {X} less mana next turn. (X=number defined on the card)(Effect only activate when played from the hand)
Secret
This card remains hidden until its trigger condition occurs, revealing it and triggering its effect.
Silence
Removes all card text and enchantments.
Stealth
Minions with Stealth may not be the target of attacks, spells or abilities until they attack. Once they do, Stealth is removed.(Stealth will still be affected non target spells such as Consecration)
Spell Power
Your spell cards deal {X} extra damage. (X=amount of spell power)
Summon
Creates a creature under your control with the specified attributes.
Taunt
Enemies must attack this minion.(This includes hero weapon attacks)
Transform
Changes a minion into something else irreversibly.
Windfury
Can attack twice each turn.