The short definition
A Veblen good is a luxury good for which demand goes up as the price goes up. That runs against the ordinary law of demand, so on a chart its demand curve slopes upward instead of down.
The usual explanation is status. A high price makes the thing a status symbol, and part of what the buyer wants is for other people to know what it cost. Luxury cars and certain watches are the textbook examples.
Where the name comes from
The American economist Thorstein Veblen described conspicuous consumption, spending as a way of seeking status, in The Theory of the Leisure Class in 1899. Keeping up with the Joneses is the same idea in plainer words.
The term Veblen effect came later. Harvey Leibenstein used it in a 1950 paper on bandwagon, snob and Veblen effects in consumer demand, which treated them as cases where what people want depends on price or on what other people buy.
Veblen goods, Giffen goods and the snob effect
A Giffen good also sells more as its price rises, but for the opposite reason: when a staple gets more expensive, people who can afford little else buy more of it and less of everything pricier. No status is involved. A Veblen good is wanted because the price is visible.
The snob effect is a cousin: preferring something because most people don't have it. A positional good, something few others can own, is often a Veblen good for the same reason.
The criticism
Economists have called conspicuous consumption wasteful, a kind of spending that buys rank rather than use, and it puts unequal wealth on display. The counter-Veblen effect describes people who do the opposite and show off how little they paid.
A Veblen good with nothing attached
Most Veblen goods still do something. A luxury car drives and a watch tells the time; the price only adds the signal. Forget Your Credit Card removes the object and keeps the signal. You pick a monthly amount from $1 to $1,000, Stripe bills it, and confirmed payments count toward a public Lifetime board if you choose to appear.
There is no product, no reward and nothing coming back. The rank only says how much you forgot, which is about as pure a test of Veblen's idea as a website can run.