A Veblen good is a good for which consumers' preference for the good increases as the price increases, and decreases as the price decreases. This is called the Veblen effect. Demand can behave in the same way as for a Giffen Good, but for very different reasons: the types of products, and the effects on demand, can reasonably be regarded as opposites.
Veblen goods are bought, wholly or largely, to show wealth: they are things primarily bought to show-off. If the price decreases, then more people can afford them and they become less effective as an indicator of wealth, so demand falls. The motive for buying Veblen goods makes them a type of positional good, but most positional goods are clearly not Veblen goods.
The Veblen effect is one of a number of effects that link preference (which is normally regarded as constant despite changes in price, as price does not usually affect utility. In this case price does affect utility. In the case of the snob effect the quantity bought reduces preferences, and in the case of the bandwagon effect the quantity bought increases preferences for the good.
There are no goods that been proved to be Veblen goods, and real Veblen goods may not exist at all. However, it is worth remembering that, for many decades, there was no strong evidence that there were any Giffen goods either. In both cases it is hard to prove, and there are many goods for which a plausible case can be made that they are likely to be Veblen goods.
Part of the difficulty in proving that a good is subject to the Veblen effect is that most goods are also subject to substitution effects and it would be hard to find examples of the price of a good changing while the price of substitutes were unchanged, and without the Veblen effect being masked by the income effect on the good — the likely Veblen goods are luxury goods subject to strong income effects.