Microsoft Core Library, ie they are at the heart of everything.
There is a more "massaged" explanation you may prefer:
"When Microsoft first started working on the .NET Framework, MSCorLib.dll was
an acronym for Microsoft Common Object Runtime Library. Once ECMA started to
standardize the CLR and parts of the FCL, MSCorLib.dll officially became the
acronym for Multilanguage Standard Common Object Runtime Library."
From http://weblogs.asp.net/mreynolds/archive/2004/01/31/65551.aspx
Around 1999, to my personal memory, .Net was known as "COOL", so I am a little suspicious of this derivation. I never heard it called "COR", which is a silly-sounding name to a native English speaker.