Every unit and structure, when attacking, has to undergo an Attack Animation. For example, when Crystal Maiden is attacking an enemy unit, she first has to lift up her staff and swing it at the target enemy unit (Damage Point), releasing the projectile, and then revert back to her normal pose(Damage Backswing). The Damage Point and Damage Backswing, when referred to together, is called the Attack Animation of a unit/structure. Similarly, the Casting Point of a unit is the part of the Casting Animation.
The Damage Point of a unit is the point, or the part of a unit's attack animation, before the attack inflicts damage to an enemy, or in the case of a ranged unit, before the projectile is released. Measured in seconds, it refers to the period of time between the attack starts and the attack lands/projectile release. When your attack is landed/projectile has been released, both Attack Cooldown must pass before next Damage Point can start. Attack Cooldown starts simultaneously with Damage Point.
The Damage Backswing, or rather Damage Backswing Point, of a unit, is the point when the attack finalizes. It can also refer to the part of a unit's attack animation after the attack lands or releases the attack projectile. Because the attack backswing serves no purpose other than to look nice, and sometimes even serves as a liability as the unit must stand still to complete the backswing (bad in situations such as when chasing a fleeing hero), the attack backswing is often canceled in techniques such as Animation Canceling and Orbwalking.

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