Erasure is the process of eliminating something from existence, an ability used by Players, Reapers, and Noise. If a Player is defeated by Noise, they are Erased; likewise if a Player is Erased specifically by a Reaper or another Player. Reapers can Erase Players if they pose an immediate threat to the running of the Reapers' Game or if the all Players fail to complete a given day's mission. If a player defeats a noise or a Reaper, it is Erased.
Note that a Player will also be erased if they don't have a partner within a certain given amount of time. At the start of the week, if a Player doesn't partner up, they will be erased for this reason.
It's possible to save a person shortly after their erasure by transferring their Soul into a Pin. This can be taken a step further by making the Pin into a Noise. This procedure can only be undertaken by Reapers or Angels, as they are the only ones who seem to be able to transfer Soul and create Noise.