What is com.apple.mail.plist and why was it slowing Mail down?

Solution 1:

com.apple.mail.plist is a property list that stores your defaults (preferences) for the Mail application.

Deleting the file meant that Mail.app would on next launch use the factory defaults.

Why your instance of Mail was misbehaving, I can't tell you, but deleting the prefs sometimes helps in these cases.