More specifically, Nigger Rich means you temporarily have a wad of money, enough for something flashy but not enough to actually change your life long term. I.E. You can get a new X-Box, but you can't move to a better housing situation. You can get a new car, but can't afford to go to school.
It also implies some things about the the things its spent on, specifically high-depreciation items like cars, electronics, designer clothes, and jewelry. Others have also pointed out that you can afford something like a fancy car but not maintain them. Or my favorite, they blow it on the down payment for a lease but can't keep up with the monthlies.
If you see someone living in a dirty, dingy apartment with rat-chewed carpet, or a moldstreaked house just this side of condemned, but they have PS5 with a 75-inch 4K UHD, that is Nigger Rich. A woman with a gucci bag but wearing walmart sweats. A dude wearing some Versace but his washing machine is broken. 90" TV with surround sound, but they getting their power switched off for non-payment. Or a rusted-out oldsmobile with $10,000 rims and a $5,000 sound system. Buying Henessy at the licqour store but has to wait for food stamps before they can get milk. Think of Bros in a your average off-campus Frat House. Or Weebs getting their first computer janitor paychecks and they blowing it all on Funko Pop and imported anime figures.
Usually Nigger Rich implies a one-time infusion of cash, but it can mean someone who got a raise or otherwise came into money, but instead of saving or investing, they are blowing it on shit that isn't worth a 1/10th what they paid for it once they get it home.
Expanding on this a bit more, Nigger Rich - more aptly Ghetto Rich because the Nigger here applies of all skintones and ethnic origins not merely African - comes from a poor-person mentality of 'use it or lose it'; they are so used to never having money and always owing that they don't know how to handle a positive bank balance. They never learned separate wants from needs, or otherwise budget. In the mind of the Nigger, any money you have after paying bills is money to blow on frivolous little luxuries because usually its too small to bother with; once the Nigger comes into serious cash this mentality doesn't change, so the only thing that changes is the price tag of the stupid shit they are blowing their money on.
And you might as well spend it quick, because if word gets around you have unspent cash, you are likely to get robbed or friends/family that lent you money might show up to collect. 'Naw nigga I don't have that 20 you lent me last week, but you can come play some Madden.'
(and again, I'm using capital-N Nigger here to denote the wider population of Niggers that includes any poor, stupid whites, spics, wops, dagos, micks and chinks. Cause this behavior is definitely not unique to little-n niggers. You'll see it in the trailer park and the barrio as much as in the projects)
A bit more sucinctly, Nigger Rich is spending money on short-term wants for the endorphin rush instead of saving for long-term needs because that's boring and acting white.
Nigger Rich spending implies a lack of forward thinking and planning for the future, which is pretty much the definition of the Tranch.