Its the backstory that goes along with them that also makes them a Hero class. They are in fact fallen heroes of the Lich King.

This was what irked me at the introduction to a "hero class" in the game--weren't we ALREADY heroes? Wasn't that the intent; that we were transitioning classes to be like the available heroes from the RTS games?
Wasn't the intent that we could be like Jaina, Maiev, Malfurion, Tyrande, Rexxar, or Thrall if we wanted to?
I already felt that if you rolled a dwarf warrior that you were for all intents and purposes, a Mountain King in the game--they can both Thunderclap, after all!

"Hero class" is just nomenclature. The name exists only to differentiate Death Knights from the "base" classes. In City of Heroes we have Epic Archetypes. Same thing: a reward for players, who have gotten a character to a certain level. They get a new class to play with and the class has a specific storyline. Nothing more, nothing less.

Fallen heroes of the Lich King?

Uh, no. The intro video makes it clear you were a hero of your faction who was killed, and raised by the Lich King.

The first original plan was for Hero classes to be new secondary classes that the original classes could then become, EG the job progression system in Ragnarok Online. Thus hero class meant something at that time, but now about as meaningless for modern WoW as 'buff class' and 'pulling class'.

in pen and paper RPGs hero classes or prestige classes are advanced classes you can't start with but have to gain certain levels in.

For example, in the WoW RPG, to be a DK, you need to meet the following requirements:

Requirements
Alignment: Any evil.
Affiliation: Scourge.
Base Attack Bonus: +5.
Class: Must have 5 levels in paladin (except in very rare circumstances).

So if you play a Good alignment, are not a member of the Scourge , do not have a base attack bonus of +5 and are not a Paladin, you can't be a DK (unless the GM says ok).

So a player who wants his character to be a DK has to make his character become this: having the evil alignment, joining the Scourge, getting the attack bonus up to +5 and being a paladin.

Blizzard seems to have rejected the "minimum level [X] as another class" concept and merely started the DK as level 55.

Makes sense. What would a level 1 DK do?

Quest Giver: Kick 10 puppies and cast Death Coil on 8 cats. Reward: 30 copper, 200xp.
level 1 DK: /sigh