Attack animation

Every unit in Dota 2 has an attack animation. This is a period of time required to perform an attack. During this time the unit generally cannot perform any other actions simultaneously, including moving. There are two components: a foreswing (or attack point), which takes place before an attack lands, and a backswing, which takes place after. The animations can be manually canceled by players, but AI units generally do not. The backswing can be canceled with no consequences, so it is always preferable to do so. However, canceling the foreswing will cancel the attack. Different heroes have different animation times, which affect their abilities to last-hit, deny, and attack enemy units when chasing.

Both attack point and backswing are reduced by the increased attack speed (IAS) attribute following the attack speed formula: 
 * attack point = (base attack point) / (1 + IAS)
 * attack backswing = (base backswing) / (1 + IAS)

 Where IAS is a percentage between -0.8 and 5.00.

With being the only exception (increasing attack projectile speed by 500), the speed of ranged attack projectiles cannot be altered. They can neither be hastened up, nor slowed down.

A unit's attack speed is completely independent of its attack animation. Attack animation strictly refers to the delay between when an attack order is issued and when the attack is launched. For example, if a unit has an attack time of one second, an attack point of 0.3 seconds, and an attack backswing of 0.5 seconds, they will be idle for 0.2 seconds during every attack cycle. Even if the backswing is canceled after 0.2 seconds, the idle period is extended to 0.5 seconds. However, during that idle period, other commands can be issued such as moving or casting spells.

In other words, canceling your animation does not allow you to attack faster.