Discriminative classifiers construct from training data the optimal (w.r.t some choice of loss function) decision boundary between classes. A query point is then classified according to which side of the decision boundary it lies on. They are called discriminative because that is what they do, they discriminate between classes.
Generative classifiers attempt to model the unknown data distribution, i.e. the distributions of the classes. A query point is then classified according to which class distribution it is most representative of.
Now consider the case where one has many training observations:
Because in the discriminative case the optimal boundary is found, as the number of observations increases discriminative classifiers are provably convergent to the best possible classifier.
On the other hand in the generative case a data distribution is estimated, and the choice of model distribution may not (in fact, most likely will not) exactly match the true distribution of the data. Clearly a generative classifier can only be optimal when the model distribution matches the true distribution of the data, and this is the sense in which discriminative classifiers are often said to be superior to generative classifiers; the asymptotic loss of a generative classifier is typically higher than that of a discriminative classifier.
BTW the paper by Andrew Ng linked to by @Matt Krause is very well known, and certainly worth a read. He examines the effect of training set size and demonstrates that generative classifiers can converge more quickly to their (higher) asymptotic loss, i.e. can be better when there is little training data, but in the long run discriminative classifiers overtake their performance.