Suppose these 3 assumptions hold true:
- People vary in the extent to which they possess some desirable quality (intelligence, wealth, perseverance...).
- It is difficult to directly observe to what extent people have said quality.
- The extent to which you have said quality strongly affects how much it costs you to engage in some observable activity - the more of that quality you have, the less the activity costs you. (Not necessarily in monetary terms).
However, one thing that less wealthy people can't easily fake is how much they can afford to spend - especially on patently useless stuff. So you can wear expensive suits, sport expensive watches, buy people expensive drinks, collect expensive art... While everybody has an incentive to "signal" to others that they're wealthy in any available way, the less wealthy you really are, the more disincentive you have to publicly burn through a lot of your own money - which is precisely what makes this such a credible way of signalling how wealthy you are.
The practice of spending money on useless stuff (aka luxury goods) to display economic power is called conspicuous consumption.
Signalling is a very useful concept to be familiar with, as it can be used to explain many puzzling behaviours. Do people get tattoos simply because they think they look good? Other kinds of body art have the advantage of being reversible and of not being so painful to acquire, but maybe the irreversibility and the pain are part of the point!
Evolutionary biology and economics cross-polinate a great deal (Charles Darwin was very explicit about the role that Adam Smith's work had played in his developing the theory of evolution), and a line of theoretical investigation in evolutionary biology that emerged in the 70ies is now known as signalling theory.
The prototypical example of signalling is the peacock's tail. The size and extravagance of male peacocks' tails is puzzling, as it doesn't serve any apparent function - in fact, their tails make them more vulnerable to predators and are therefore a handicap! But biologist Amotz Zahavi proposed that such handicaps could work just like conspicuous consumption (another good phrase to remember: the handicap principle). The signal conveyed by such a handicapping trait would then be "I'm tough enough to survive in spite of this".
Such handicapping traits could then become more prevalent and more extreme over the generations through the mecanism of sexual selection: some portion of females desire that trait, which makes having the trait advantageous for males - which makes it advantageous for females to prefer that trait! (Their baby boys will likely share it...) As the trait becomes more prevalent among males, the competition gets fiercer, and the males that pass on their genes will tend to be those who are highest on that trait. This kind of runaway process through which non-adaptive traits become more prevalent is called a Fisherian runaway.
It's easy to go overboard with this and start overconfidently diagnosing all sorts of phenomena as instances of costly signalling. Whether the above explanation for the peacock's tail is correct is not at all clear. Another domain of costly behaviour for which signalling accounts are being controversially discussed is religion. Likewise, signalling is believed by many to play an important role in art, another classic example of an evolutionarily puzzling human phenomenon.
Evidently, what stands out about signalling is how frickin wasteful it is. Scenarios in which competition leads to ever costlier signalling are, indeed, examples of market failure - cases in which the self interested actions of individuals lead to an inefficient allocation of resources, in the absence of any coercion.
More precisely, one individual's costly signalling, while advantageous to that individual, has a negative externality, i.e. a cost that is incurred by people other than the individual engaging in and benefitting from it. Why is that? Well, by engaging in this costly signalling, he has made the competition tougher for others, meaning that they will now have to engage in even costlier signalling in order to get the same benefits.* So while everybody individually benefits from their own signalling, everybody is worse off than if nobody had engaged in it at all.
More on this last point shall soon follow.
* Note that a crucial point here is that the signalling behaviour is wasteful, and thus the competition between signallers engenders more and more waste. Somebody who accepts to work for a low wage also makes the job market a bit tougher for other job-seekers, however since no resources are wasted, this is not a case of market failure.
Economics is hard :)