What is a Living National Pokedex?

Let's break this term down into it's constituent parts, first I'll explain the Living Pokedex, the I'll explain the National Pokedex, then we'll put them together to understand what is meant by the term Living National Pokedex

Living Pokedex

In the Pokemon games you are given a special tool that keeps track of which Pokemon you've seen and caught, that tool is called the Pokedex. To complete the Pokedex you have to catch 'em all, as the saying goes. Completing the Pokedex, however, does not require you to own every single pokemon at once. For example, if you catch a Pikachu, your Pokedex will show that you have caught a Pikachu. If you evolve that Pikachu into a Raichu, you will no longer have a Pikachu, but your Pokedex will still show that you've caught both. Additionally, if you trade a Cubone to someone for a Chansey, both Pokemon's entries in the Pokedex will be complete, even though you no longer own a Cubone. The living Dex is a unique challenge where you must own a copy of each pokemon at the same time in order to complete the challenge. This means you would need to catch two Pikachu's and evolve one of them. This is true for each pokemon and all of their evolutions.

National Pokedex

With every new Pokemon game comes a new generation of Pokemon invented just for that game (or as the games describe it, these pokemon have been discovered). The region in which each game takes place always has every Pokemon from that generation of Pokemon, but only has a few Pokemon from previous generations. For example in Gold & Silver Mewtwo is unobtainable. This lead to the existence of the Regional Pokedex. In order to complete the Pokedex in any game you only need to complete the Regional Pokedex, meaning you would not need a Mewtwo in order to complete the Pokedex in Gold & Silver. This is where the National Pokedex comes in. In order to complete the National Pokedex you need to complete the Regional Pokedex and also catch all the Pokemon from previous generations, by trading from other games. For example, in Gold & Silver you would need to catch every pokemon from the first two generations in order to complete the National Pokedex. Completing the National Pokedex does not require owning a LIVING copy of each Pokemon.

The Living National Pokedex is hopefully self explanatory now but let's review:

Living Pokedex: A collection of every single Pokemon in a game's Regional Pokedex

National Pokedex: A Complete Pokedex of all Pokemon from every generation prior to and including a given game's generation. The national Pokedex does not require a living copy of each pokemon, only that you HAVE had them at one time or another.

Living National Pokedex: A collection of every single Pokemon from every generation, up to and including a given game's generation.