Evade is a new mechanic for the Diablo series on PC but was available on the console version of Diablo 3.
Evade allows the player to swiftly move and evade an attack with the push of a button. This function is available right from level 1 of a character.
Blizzard has stated that the Evade function now allows players to take on tougher enemies earlier on in the game while they are building their character out.
Evade is indicated by a small foot icon next to the resource globe. In the example below it is bound to the spacebar key.
Gear and Evade
Gear you equip can impact your Evade functionality, specifically boots.
For example, some boots may give you an additional charge to your Evade ability allowing you to Evade twice in quick succession.
Evade and Obstacles
Evade does not allow players to pass through objects or obstacles they encounter. It is specifically a dodge mechanic.
Evade also does not break crowd control (CC).