(noun) Someone with a lot more money than you. As such, the definition is elastic depending on one's economic status. Usually a term applied to others rather than to oneself.
In addition to its more common usage, rich can be used to describe objects of luxury or cool things such as shoes, shirts, cars, houses, jewelry, etc.
"Sick Lambo man, that is rich!"
"Nice shoes man, those are rich."
"I'm rockin a bar of gold attached to a platinum chain, don't tell me that ain't rich!"