The kernel trick and support vectors
The authors showed that a maximum-margin linear classifier can be applied to nonlinear problems without ever constructing the high-dimensional space explicitly.
Why it matters
A method with proven guarantees appeared that, in a paired paper by the same authors (NIPS 1992), compares favourably with backpropagation networks on handwritten digits, and networks were set aside a second time for a decade.
A kernel function computes an inner product in feature space without building the features, so classification time is linear in the dimension of the input, not of the feature space. The training problem becomes convex, meaning it has a single optimum, unlike networks where the result depends on initial weights and chance. That reproducibility is what made support vectors the standard of the 1990s.