Remnant is first properly seen in "Special Delivery". While in camera mode (older versions) or you find a certain spot on the map, remnant can appear on your device. The player can either use the flashlight to draw the remnant towards them, or walk up to them with their device. 

Remnant comes in a variety of different colours. White, red, green, purple, gold and rarest is rainbow. At the same time, they are protected by shadow remnant, which is drawn by the flashlight faster. This results in the screen being "infected" by the remnant, but wears off as long as the player avoids to collect more of the bad remnant. Collecting too much dark remnant will result in an encounter with Shadow Bonnie. Defeating him will result in more remnant being given.

In older versions of the game, the player can lose any remnant that they have not used after being jumpscared by an animatronic. This is no longer the case.

Remnant can be applied to the animatronics to make them stronger in salvage and combat. Remnant cannot be removed once it was applied to an animatronic, though its easy to gather more and even increase the amount gained with devices. The maximum amount of remnant that an animatronic can hold is 100,000 units.

The books help to explain a bit more on what Remnant is and what is does. In Fazbear Frights, remnant is described as a silver, bubbling liquid that can also be molded into actual objects.

Talbert, who studies remnant explains that it's a haunted metal that is made to preserve the memories of the once living, even after death. He made a heart shaped pendant made out of this substance to keep his sick daughter alive, so that he would "never lose her". This implies that remnant is what makes things come to life, and can be applied towards corpses and animatronics.

Eleanor used the same heart shaped pendant for her goals. It was not only used to disguise herself as Renelle to get actual remnant, she used it to trick Millie in To Be Beautiful. What's worth noting is that despite Eleanor slowing turning her into a robot, Millie didn't die until the pendant was removed from her. Furthermore, Millie and the others couldn't see her true altered form until her death. This means that not only remnant keeps someone from dying, but that remnant also acts like an illusion disc, which was first mentioned in The Twisted Ones. However, in TTO, the discs emit a high pitched noise, where the pendant emitted a singing voice.

In The Ultimate Guide, it's explained that remnant holds the key of power and eternal life. It also confirms a theory that William dismembered the animatronics in FNaF 3 to get the remnant out of them for the Funtimes, which later became Ennard. This also means that objects infected with remnant can be taken out and reused many times for other things.

This theme of remnant being a haunted metal isn't too farfetched in the FNaF universe. One of the distorted robot sounds in FNaF 1 is a stock clip that was a reversed reading from "The Autobiography of a Yogi". In that very clip, it was a reading of a paragraph where it argues that metal has a life force, just like how plants and animals are living things. This brings forward the theme of "haunted metal" in the FNaF universe. It may or may not coincidentally be an inspiration for remnant and it being applied to robots.