From the Gospel According to Matthew, Chapter 27:
    6 And the chief priests took the silver pieces [the bounty on Jesus, donated by Judas], and said, It is not lawful for to put them into the treasury, because it is the price of blood.
    7 And they took counsel, and bought with them the potter's field, to bury strangers in.
Herein we find the biblical origin of the term "potter's field", as a specific graveyard, located south of Jerusalem, for those who died away from home or with no family or friends to bury them. (Acts 1:18 refers to this field as well, though only in passing, and does not note its intended purpose. In its defense, the second half of the verse is more interesting, in which Judas falls over, explosively disemboweled.) The association with Judas and his blood money left the field at least aesthetically tainted, and it was accordingly named Aceldama, "field of blood".

In any case, no one can resist a biblical reference, and the term came to refer to any public or charitable burial ground for unknowns, undesirables, the destitute, or unclaimed corpses. Obviously, the exact method of interment will differ according to expense, soil quality, practicality, and such considerations, but while there is no guarantee of an individual burial plot, potter's fields are generally not considered mass graves, with the latter term implying creation for purposes of convenience (be it a matter of genocide, plague, or whatnot), while the former implies more of a sense of obligation, a desire to respect the dead, even those unknown in life.