Well, when Pokemon first came it out in 1997(?), Pokemon's main audience age ranged from 6-12, something like that. It hit that audience right at the heart, incorporating an easy, child-friendly RPG and letting the imagination just roam wild.
It just caused all this commotion and Pokemon became the newest fad. You could do so much with Pokemon. And there were cards that were just as entertaining as the games, and an anime came out along with that captured the audiences even more.
The kids loved it, and at the same time, it was enjoyable to adults. That would be Nintendo's main advantage over all other consoles; it is marketable to EVERYONE. There's a reason it's held onto the rating 'E for Everyone.'
And then they made Silver/Gold/Crystal, same formula, now in color, and genders are also considered. Slight upgrades, held the audience captive, but people grew bored.
Enter new formula. IVs, EVs, Natures, better graphics, completely new storyline, new battle system (Double Battles), new place to battle (Battle Tower/Frontier), it basically went nuts. Pokemon went into overdrive, growing with its original audience who were now mainly in their early to late teens, but still allowing the newer audience to enjoy Pokemon on the exact same level. This is what Ruby/Sapphire/Emerald/FireRed/LeafGreen brought to the table.
But then, they did it again, only this time, much better. Diamon/Pearl/Platinum/HeartGold/SoulSilver devised an even more clever battle system, and made the graphics much better. Physical and Special split, EVs and IVs were something that actually mattered, basically, these changes made the game even more playable to the older audience. It added enough to make it competitive to other RPGs, without losing its original essence. At this time, it was still the same game that those 10 year olds in 1997 picked up, but had the ability to be something that a 20 year old who was much wiser, and much more strategic could play.
And Black and White basically took everything good about Pokemon and made it better. Basic formula, except much more in-depth, much more thought out. All the while still being the same game that the 10 years olds once picked up, and still playable by younger audiences and newcomers.
Pokemon is one of the few universal games out there. No matter your age, Pokemon can still be appealing, and you have all the benefits of an RPG (except create your own character). It's just garnered the reputation of being a children's game.