Evolution is the permanent transformation of a Pokémon into a different, usually stronger species, most often on reaching a set level, with other triggers including stones, friendship, held items, location, and time of day. Evolved forms have higher base stats and often new types and moves.
Level up evolution is the backbone of a playthrough. Charmander becomes Charmeleon at level 16 and Charizard at level 36, gaining a second type on the way. Most three stage lines follow that pattern, and the final stage is usually where the stats justify the wait. Pseudo legendary lines make you wait longest, with final evolutions as late as level 64 for Hydreigon in Generation V.
The other triggers are where the games test whether you read the fine print. Eevee alone covers stones, friendship at different times of day, location based evolution in Generations IV to VII, and a move based trigger. Inkay evolves only while the console is held upside down in its debut games. Milotic required contest conditions in Generation III before later games switched it to holding a Prism Scale in a trade. Meltan evolves only in Pokémon GO.
Evolution can be stopped. Pressing the cancel button during the animation, or having the Pokémon hold an Everstone, keeps the current form, which players do to learn moves earlier, since unevolved Pokémon often learn moves at lower levels. Delayed evolution trades short term stats for a better movepool, then evolves once the move is learned.
In play"Hold off on evolving that Eevee until you know which form your team actually needs."