Major spoilers to follow: who woulda thunk that Signora Laurentini was hiding out in the convent the whole time? There's all that guilt Agnes/Signora Laurentini is still carrying from her role in the Marchioness's death, all those years ago:
"What are years of prayers and repentance? They cannot wash out the foulness of murder!" (4.16.11)
That's some serious fire and brimstone.
The sight of Em's face bring Signora Laurentini lots of pain, but it's almost kind of therapeutic. Em's a dead ringer for the woman she murdered. Everyone the Signora hurt has been dead and gone for a long time. Signora Laurentini knows she can't make amends for what she did, but she can finally tell her secret to someone connected to those awful crimes.
What's more, Signora Laurentini feels like she owes Em some kind of monetary payment, in the form of the Castle Udolpho. Does it bring her any peace? Maybe not, but it's a start.