Why are there Sibyls and Prophetesses in the Sistine Chapel? For what purpose did Michelangelo add each Sibyls or Prophetesses to the ceiling of the Sistine chapel?
This is an explanation to why they're there in the first place.

The latter, although belonging to the pagan world, are represented here because of their prophetic gifts, in this way extending the wait for Redemption from the chosen people to all mankind.

I'd imagine they each have some sort of story - or at least represent some different part of the pre-redemption world and pointed in some vague way to Christ.  But what is the vague way?
Here are the Sibyls:

Erythrean Sibyl

Persian Sibyl

Libyan Sibyl

Cumaean Sibyl

Delphic Sibyl


Source
There is a history to those Sibyl.
First of all, the word Sibyl means Prophetess, and this word was originated from Greek.

Erythrean Sibyl appears as the one who has prophesied the Redemption in arts.
Persian Sibyl seems to be the priestess who occupied over Apollo Oracle.
Libyan Sibyl was priestess who was the presiding over Zeus Ammon Oracle.
Cumaean Sibyl was the pristess who were the head of the Apollo Oracle at Cumae.
Delphic Sibyl was a figure who made prophecies at Delphi.

In short, they are in a way not related to the Christianity. However, the reason for them to be depicted at the ceiling is because some of their prophecy was in a way related to the prophesying the coming of Christ. For example, Cumaean Sibyl was told to be declaring a new progeny of Heaven would bring about a return of the &quot;Golden Age&quot;. This was thought of prophesying the coming of Christ.