On each hero card, there are 3 cubes that seem to outline the concentration of the hero, but I cannot find a explanation for them nor any application of them in-game. Can someone help me? I just received the game, and am getting the impression that the heroes can equip any weapon or rune regardless of class.

Those are the power dice that the hero adds to his attack roll when making an attack of that type. They're mentioned on page 10 (under Attacking, Step 3) and page 11 (under Types of Attacks).

For example, if Battlemage Jaes makes an attack with the Immolation shop weapon, he rolls the dice indicated on the weapon card (white + green), plus his magic trait dice (2 black), because it is a magic weapon. So his combined roll is 1 white, 1 green, and 2 black dice.

...and to confirm your impression: Yes, any character may equip any item, weapon or rune (barring a few restrictions for runes on heavy armor) within in the limits stated in the rules.

It isn´t, however, always sensible that a hero with three Magic trait dice attacks with a Melee weapon...

Nice, thanks a lot! I'm glad to have those questions cleared up?