This comic also helps sum it up a bit:
awkwardzombie.com/index.phpAs for the games themselves, they do tend to have more of a focus towards kids given their storylines and generally easy difficulty... but that's the 'story mode' of the whole thing really.
After that's done with and completed, there's often more difficult challenges available to conquer, and then there's proper, competitive battling. Battles can be quite complex when fighting other humans rather than AI, as it's battles of six on six, and each Pokemon has it's own type of elements, strengths and weaknesses, and four moves.
No two battles are the same. Sure you could switch that Grass type in to fight that Water type, but it might have an Ice attack that Grass is weak to, so you might have to time it carefully... and there's a chance they could switch in a Fire type that Grass doesn't like either. Let alone each Pokemon being built differently, some are fast, some are slow, some hit like a truck, some take hits like a truck. There's a bit of luck and a lot of tactics involved when playing competitively.
Also there's the breeding aspect which some people go for. There's things called IV's (
Initial Values) which add extra points to each stat, and are influenced by a Pokemon's parents, kind of like genes, and as such many people, especially professionals, try to breed their Pokemon to have the best IV's/genes available to get every bit of an edge in battle as they can.
The community known as Smogon is where most competive battlers reside and discuss tactics in particular:
smogon.com/So it works for all ages really; the story mode and stuff works well for the kids playing around, where for adults there's more meat to be found via other challenges, breeding, and competitive battling.