The UV Light in Phasmophobia is used to reveal a ghost's Fingerprints and Footprints. Keep in mind that Footprints are not Fingerprints and do not count as journal evidence.
Finding a Ghost's Footprints with the UV Light is more likely after a ghost has stepped in Salt, and all Ghosts have the ability to step in Salt. This can be useful if you are trying to position Motion Sensors for an objective.
The UV Light can be used with the lights in the room turned on, though it is often much easier to see the Fingerprints and Footprints if you have the other lights turned off.
You can find Fingerprints on closet doors, doors, light switches, windows, cell doors (the keyhole or the food/hand slot). When you find Fingerprints (or full hand prints) take a photo. Each photo of a different hand print/fingerprint is worth a few bucks.