It is an attack on one primary target or on one target + N random targets.

Examples: Astoria's basic attack “Stars behind the Clouds,” Oakley's 2nd special attack “Cardsharp's Hand", Omphis's basic attack "Burst of Chaos". 

Artifacts: If the hero's ability description states that the attack hits one target and + N random targets, the damage is only increased from the hit on the selected target.
However, if a single attack is a multi-attack, the artifact increases the damage from each hit on the selected target.