By default, heroes and allies can only do one explicit attack action (via clicking ATTACK or drag-targeting for an attack) before being exhausted. If more explicit attack actions are possible, it is specified.
Attack x times is a specific term reserved for heroes and allies (and items that become allies).
Grant the hero or the ally to perform x multiple attacks during one player's turn.
The cards that give the ability to perform X attacks are regrouped in three keywords:
some with may or can attack …;
few with readied;
one with each time an item or ability is targeted and destroyed.
note that if an effect causes an ally/hero to attack automatically then that does not exhaust the hero/ally (and it can happen if they are exhausted)