[RPG] What does a Template mean by Hit Dice

Generally, template describes the situation if there will be any Hit Dice size change . Wizards online Types and Templates defines this as follows (along with changeing Constitution score)

Before applying any Constitution changes, check the Hit Dice and Hit Points entry in the template. Some templates change the number or size of the creature's Hit Dice or both. Some templates change previously acquired Hit Dice and continue to change any additional Hit Dice the creature gains. Most templates, however, change only the creature's racial Hit Dice (that is, the Hit Dice it has before adding any class levels). Most templates are fairly explicit about what happens to the creature's Hit Dice, so just follow the instructions in the template.

When you know the size and number of the creature's Hit Dice, recalculate the creature's hit points using the modifier from the creature's new Constitution modifier for each Hit Die (whatever its size).

In your example, you re-roll hit dice with new hit dice size.

UPDATE:

From D&D 3.5 Monster Manual Hit Dice entry description:

This line gives the creature’s number and type of Hit Dice (the die rolled to generate hit points), and lists any bonus hit points. A parenthetical note gives the average hit points for a creature of the indicated number of Hit Dice.

D&D generally defines base HD and additional HP (CON bonus and other bonuses if available) for creatures, but also offers a pre-calculated value for HP of that creature. So you can either calculate it or use pre-calculated value.

That means, game mechanics leave the final decision to DM (in most cases), and it is up to him. (Such as; in my games, I generally offer players 3/4 of the die they roll for their HP when they level up, and calculate NPC HDs in a similar way.)

Better you discuss that with your DM and all of your players and find a way that suits everybody.

As Oblivious Sage pointed out in the comments, according to the official rules, no, you do not get any extra HD for getting a template. When you gain the template:

Hit Dice: Increase all current and future Hit Dice to d12s.

However, you do not gain any extra hit die. What you are doing here is acquiring the template bit by bit, but since there is nothing in the template to give you HD, you dont get any.

There is a reason why base creatures usually need at least 5 HD.

However, let us think beyond the mechanical ruleplaying. I am pretty sure your DM knows that a level 9 character with 12 hp would be unplayable. If so, why does he still say that you don't gain any extra HP after lvl 1? Either, he is the type of gamer to love rules above all, or, he doesn't really want you to play a vampire in his game. There is also the possibility that the DM simply trusts WotC to know their product, and to have chosen LAs fairly (Thanks, KRyan). Or, the DM is running a story-centric or social game where fighting ability balance is not important (credits to SSD). Either way, ask him about it, metagame.

If it's because your fighting ability balance doesn't matter, then you are set to go, knowing that you will only get 12 hp. If he doesnt want you playing vampires in his game, that is his call, and you will need to respect that. If he is okay with you playing one combatly, then you need to work together to make it playable, probably with a homebrew solution. Gaining d12 every level would be over the top, making it annoying to other players, however some HD progression is needed. One possibility would be to lenghten the process of acquiring vampire template by adding your class levels (and therefore gaining HD) in between your template levels. However, I am not sure of your intentions and the playability of such a build, so that might not be the what you are looking for. The other possibility is just houseruling HD progression into the template, but make sure its either not every level/not d12, and in any case, this will and should lenghten the process of acquiring the whole template.

That is why, and once again credits to Oblivious Sage, it is usually a bad idea to take Templates with high LA. I would like to point out that it may not be such a bad idea to use different PC creatures, since those usually already start with some HD. However, I do understand that your desire to play a vampire is not a quest for powergaming opportunity, so just talk to your DM and try to make your character playable.

If you took a bard level every second level, alternating between vampire levels and class levels, at 9 level you would have 5d12 hp, that is average 38 (+your con modifier x5), and you would have 5 vampire levels to go. A 9 lvl bard has an average of 34 hp, which would make you pretty balanced. That way, at ECL 16, you would be a fully vampiric lvl 8 bard, with roughly appropriate hp, and a wide array of abilities at your disposal.

Hope this helps.