A hero is able to evolve once its six of his or her equipment slots are filled.
Each equipment gives some bonus to a hero when it is equipped; you can only equip certain equipment specified though. You can't choose which stats you want to add; like other RPGs.
All the equipment is sacrificed to permanently add their stats to the hero. The items do not return to your bag; their stats are affixed permanently to your hero.
The hero also gains additional bonus stats. The bonus stats gained is 2 * (evolution stage) each for STR, INT and AGI. e.g. White to Green is stage 1, it gives 2 STR, 2 INT, and 2 AGI. Green to Green + 1 is stage 2, it gives 4 STR, 4 INT and 4 AGI. Altogether, it gives 6 STR, 6 INT, and 6 AGI from White to Green + 1.
The stats gained from equipment does not include bonus from enchantment. If an equipment is enchanted, you are partially compensated with the enhancement points in whetstones.
The items required for later evolutions add more stats. However, the rarity and level required for them are also higher.
An additional skill is unlocked when a hero evolves into a different color.
Other than choosing a equipment which you like to enchant to the max (to add more of a stat you like), there is not much benefit from choosing not to evolve your hero.