Scrolls are a vital tool used by all shinobi in the Senran Kagura series. Their primary use in the series are for techniques such as Shinobi Transformation and Secret Ninja Arts and thus every shinobi must have one on them at all times.
Secret Ninja Art Scroll
A Secret Ninja Art Scroll is where a shinobi borrows the powers of Nature so as to exceed their limits. In order to use Secret Ninja Arts one must first enter their Shinobi Transformation state (also called Yang Mode) by using the scroll or enter Frantic state (also called Yin Mode). Each shinobi keeps their scroll hidden on them in different places to prevent it from being stolen by their enemies. Losing the scroll means losing the ability to transform and access your Ninja Arts.
Super-Secret Ninja Art Scroll
A Super-Secret Ninja Art Scroll represents the essence of a shinobi school. Each school only has one and regards it as their treasure. Drawing on the powers of Yin and Yang allows a shinobi to release his or her full potential. These techniques cannot be used by everyone, however. Those lacking enough power will find themselves unable to read what is written in the scroll. As revealed in the Crimson Girls story of Senran Kagura Burst, spiritually weak individuals who attempt to use the ultimate Yin Techniques will be driven mad, if they can read it at all.
Hanzō National Academy is revealed to actually have two of these scrolls after one is stolen during the events of Senran Kagura Burst. Asuka and Homura later use these two scrolls to unlock their Awakened forms, Ultimate Asuka and Crimson Homura.
In terms of gameplay, Scrolls are gained by filling up your Ninja Arts gauge (through dealing damage to opponents or parrying attacks), and different abilities cost different amount of scrolls to use (from one to five scrolls). The maximum amount of scrolls you can have raises as your character gains levels, with the actual max varying between games.
For gameplay purposes, even characters who are not shinobi (like some guest characters), or characters who lack aptitude as a shinobi (like Murasame) still have access to a Ninja Arts gauge and scrolls, even though lorewise they don't possess an actual Scroll.