Physical protection manifested from one's soul.

Protection

Veil is usually only visible while it's being used to prevent harm. When in use, it produces small amounts of light. Usually, it's dim enough to not notice.

Veil provides a way to prevent physical harm from an outside source. However, this doesn't stop poison, disease, or internal damage.
Your veil is tied to your will and determination, your "spirit." When your spirit is broken, so is your veil. However, your veil can also be broken by brute force. When this happens, your spirit isn't broken as well, meaning that veil is affected by spirit, but spirit isn't affected by veil.
Your veil strength can be measured by the wavelength of the light that is emitted by your veil. This is useful for battle-based sports (such as Hexabrawl), as you can tell how much of someone's veil is currently left every time they get hit using special light-measuring devices.

Veil is said to be a physical manifestation of your soul, though it seems to be more tied to your "spirit" as described in the appearance tab. This use of "spirit" doesn't mean the same thing as "soul," it means your determination, will, and resolve.