From Diablo Wiki
Purists are players who choose to eschew some elements of the game, usually ones that make things easier, with the aim of creating a more challenging gaming experience, or at least not cheating.
They may avoid common forms of cheating, cheesy techniques, or even regulation elements of the game.
Some purists refuse to trade items, twink, maphack, or mule items. In some cases or they may only play LotL style, or only use low level skills, etc. There are countless ways for players to remain pure, and it's not uncommon for players to keep some of their characters pure, while playing less scrupulously with others.