From Brotato Wiki
Bandana is an in-game item that can be bought from Shop or can be found in a Crate. Most Items increase the Stats of the player while some of them provide unique effects.
The Bandana increases the amount of pierce for projectiles by 1. This includes ranged weapons and projectiles spawned by weapons such as Cacti Club.
It is a very useful item to help single target ranged weapons keep up with large hordes of enemies.
Projectiles have a default damage falloff of 50%, unless the weapon have piercing by default such as the Laser Gun. The piercing from the bandana uses the same damage falloff as the innate piercing, and is also affected by Pumpkin
Projectiles with both bounce and pierce will only pierce after they're done bouncing.