No... what they mean is that the game has a set of rules. These rules are designed around the ability to provide a fun and challenging game. The balance is between the fun and the challenge. A game that is too difficult is a lot of times not seen as fun (especially if it is impossible) and a game that is seen as easy is a lot of times seen as fun (especially if you get a sword of godly power and get to pound people into the ground all the time).

Of course there are impossible situations where the fun is to see how long you can survive, but if the game was not balanced that would mean I could make it last 2-3 days before you are overwhelmed or 1 - 2 seconds.

I could take every monster unit in the game and give them all the hitpoints of some mites and the initiative of a turtle to boot. Won't change any abilities or rewards. You would find the game fun for awhile, but is this a balanced level of play. The game is too easy, but hey I would have fun watching my militia kill a storm dragon and can have lots of fun doing it.

Seconding I could set every monster unit to have an initiative of a rabbit and the hitpoints of twice that of any of the titans. Give every unit damage in all aspects, be it fire, cold, poison, and so forth. But if I don't change your hitpoints to match or damage to compare, it would be an impossible game to play. In fact, why not just have it in the scripts that every player starts directly next to 8 storm dragons.

So the term balance does not refer to nerf things, sometimes it refers to that other things needs to be brought up to the awesomeness. Under particular reasonable conditions a simple dagger shouldn't be able to kill a dragon on the first turn. (Not talking about a dagger of dragon slaying, but a simple rusty level 1 dagger). That would probably mean that the simple dagger needs to be nerfed or the dragon needs to be buffed. In essence, there is a correct point where fun and challenging meet. This balance is impossible to acheive with everyone and this is why you will never please everyone.

Thus, the other part of balance is within the playing community. Give enough fun element to the majority while not completely shunning the minority. This is usually achieved by difficulty settings, if I put it on Insane I should expect a challenge, and if I set it to easy it should be closer to I WIN senario everytime. But you can't have a slider for everything because then you might as well make your own game to play.

Balance can mean all these things, but also:

Balance between all the factions.  Invariably all games have some factions who are more powerful than others due to "racial" abilities that play stronger or weaker in the greater framework of an entire playthrough.  Some games are better at balancing the different factions than others.

balancing is just tweaking so that "1 that beats the alll"

here some exemple

earth mage who can raise mountains cand "I-WIN" vs non earth master in defensive play, now that less "random" it is even easier make it easier and them krax(even more powerfull now)+earth leader+ defensive you can more or less give up if you not a earth mage , really "fun" but they finnaly heard the problem and made lower land rank 1 earth

balanced a issue to counter a I-WIN-button strategy

but on other hand of the coin

Doublestrike > berserk >rush is freaklishy OP right now with upgrades from fortress " your unit get first move" make riders able to run accross the battlefield and even mid tiar (still in leather, horse a blacksmith weapon can easy beat 100+ dam) to slay almost anything (even dragons) before they get their turn...get them up to lvl 5 + perks and serious gear and such and they are a unstoppable force where even golems,juggernauts can't save you and mages never saw it comming (most cases you already have a second turn before their slow ass mage get 1 ^^'')

and look up Bm and bears,mauling dragons with a cub ^^

That is what it suppose to be but in reality when someone whines about balance they are talking about nerfing parts of the game that they don't like in favor of enhancing something they like in a game.  In MP games you will find people who were defeated in the game crying about "Balance" because they think that they are so good that they can't possaibly be defeated/killed in the game.

Balance, for me, means making sure all options have their uses.  We spend a lot of time designing and implementing the wide variety of options in the game, so its a shame if a portion of them shouldn't ever be touched simply because they are to weak, or other options are to strong.

That certainly doesn't mean all options should be the same.  They should have different pros and cons.  And I certainly don't mind that there is one better answer for a specific situation.  But each option should have cases where it is the best option.

As a designer my goal isn't to have players thinking that everything is balanced.  I want players to feel like every option is overpowered.

Yea, llamabeast has worked on the Conceptual Balance Mod for years now for Dominions 3 and a server for playing Dom 3 through email.  Good to see you here.