Before Ash introduced the idea of becoming a quote unquote Pokemon Master, and well before Competitive Battling caught on in the PokeWorld, the sole purpose of Pokemon (and we all remember) was to complete the Pokedex and "Catch 'Em All." This remains a constant even to this day, and though it is much harder than back in the day since there are now a grand total of seven hundred and twenty-one Pokemon (Wow!), you are always greatly rewarded within the mainstream Games if you achieve such an accomplishment.
Ash's dreamful idea is great, but one cannot truly be a Pokemon Master if they can't finish the ever-growing National Pokedex. And it doesn't stop there, as there are a number of trainers that take this to the extreme. Some Trainers don't just need one copy of every Pokemon, but an additional copy of a Shiny Pokemon. A Shiny Pokemon is a Pokemon in an alternate color, and they are very rare (1 in 8,000 of chance of finding one). However, Shiny Pokemon have also become easier to obtain, with the Shiny Charm and Masuda Breeding Method (Breeding Two Compatible Pokemon From Different World Countries).
These types of enthusiasts also try to obtain all Mega Evolutions, Primal Evolutions, and All Forms of Pokemon to successfully complete their Pokedex 100% (though it isn't necessary). But this way of thought also gives you a number of chances at obtaining all the Pokemon with both their regular and Hidden Abilities.
But all of this begs the question: How can one possibly complete the Pokedex with the sheer number of Pokemon alone and with the number of game exclusive and restrictions, if it even is? Well, we'll tell you...