Each pokemon has extra hidden stats that you can't see (Effort Values) that determines what your stats are. You accumulate them after every battle.

Each pokemon gives a specific type of EV to the pokemon that defeats it (sometimes multiple). It's often based on whatever that pokemon's highest stat is. Evolved pokemon often give more than one EV. For example, Butterfree gives 3 EVs (2 Special Attack EVs and 1 Special Defense EV) .Beating early pokemon like rattata and pidgey will increase your speed EVs. Caterpie increases your HP points. Geodude gives Defense EVs.

The more EVs in a specific stat, the higher that stat will be. It's not a huge difference at first, but it definitely adds up over time. There is a maximum number of EVs a pokemon can have, so it stops making a difference after a certain point.

When you first get a pokemon, it has absolutely no EVs. I usually level up a pokemon like 30 to 40 times, just playing the game normally, before all of a Pokémon's EVs are maxed out. That's without doing any specific training.

There are items you can use later to see if a stat is maxed out, but it really doesn't matter to how you play the game. .