Not exactly, you can combo attack very rarely with a few specific heroes, otherwise if you see the text Extra Turn , that is when your hero has x2 the agility if your opponent, thus he gets to do 2 turns in a row.
That is why people say that agility is the most important stat in PvP, you can get extra turns + you hit first.
that is a Good News you can attack twice... its called combo rate... you can see an Extra Rounds before it attack right? cool you can attack twice... that is something...