Attack is the default control ability on the left click in Diablo III, as it was in Diablo I and Diablo II. Attack causes a character to run to a location, when clicked. It causes the character to attempt a melee attack on a valid target, when clicked.
As was the case in Diablo II, most characters will want to substitute a more powerful special skill for Attack, at higher levels. Spell casters will likely want to put a ranged attack spell on the left click, so they do not run up to engage in the melee combat for which they are not suited.
- See the page in the Diablo II wiki for more details.