A term used, particularly in Britain, to refer to a certain segment of the
Upper Classes. If you are 'old money', it means that your family's financial assets (money in the bank, shares, and one or more houses) have been passed down for several generations, certainly since before 1900, probably before 1800 and before (in which case you are 'old, old money'). The fortune involved need not be particularly large, although it is usually enough for the recipient not to need full-time employment.
'Old money' has nothing to prove; therefore, the pressures placed on the 'nouveau riche' to automatically own Rolls Royces and expensive designer-label clothes do not apply - if 'old money' possesses these things, it is because he or she wants them, not because he or she feels a need to impress others. 'Old money' is more likely to drive an old Volkswagen Golf or an early-model Range Rover, and wear something comfortable by a obscure tailor familiar to only a few hundred people.
'Old money' can be found spread throughout the south of England - Wiltshire, Sussex, Kent, preferably somewhere with a nearby railway line leading into London - and also in London itself, around the Kensington and Chelsea area (and also, oddly, down some of the side streets off Tottenham Court Road). One or the other residence will be a second home.
The writer of the first writeup above seems to believe that 'old money' exist in America; pah!