As to what causes this:
Based on this list of Insight-related audio and visual changes:
A crying baby can be heard occasionally.
However, these changes lose their insight requirement once you have defeated Rom, which, based on your previous post, I know you have.
Now, for the why:
The reason is lore-related, and I'll try to describe it as I understand it roughly, keeping spoilers to a minimum.
The theme of birth and rebirth is present all though Bloodborne, and becomes clearer the further you progress. The description for the 1/3 Umbilical Cord items will best answer your question, but may spoil things, so don't read if you're worried about having things spoiled for you.
From what I've come to understand, the crying baby is a manifestation of the birth of a Great One's surrogate child, possibly Mergo.
Once you have completed the game (or your desire for a plot/lore explanation becomes overwhelming), I highly recommend you read "The Paleblood Hunt". It delves into the lore in extreme depth and does its best to explain a lot of mysteries.