A Shadow Attack is the (likely unofficial) name for special attacks that can be done while dashing, a feature of which was first introduced in Power Instinct Legends and has become a staple in the series since. It is simply done by executing the special move's input during the dash.
When the particular special attack is successfully done, it will leave a trail of shadows in its wake as the character performs the move. These can provide either a further range of priority, stronger blows, or land more hits. Most characters tend to have one or two special attacks which can be done while dashing.