Léon Bottou's implementation of Stochastic Gradient SVMs is the most concise implementation of an SVM that you'll find: http://leon.bottou.org/projects/sgd
"Support vector machines (SVMs) are a set of related supervised learning methods... The standard SVM takes a set of input data, and predicts, for each given input, which of two possible classes the input is a member of... Intuitively, an SVM model is a representation of the examples as points in space, mapped so that the examples of the separate categories are divided by a clear gap that is as wide as possible. New examples are then mapped into that same space and predicted to belong to a category based on which side of the gap they fall on." [wikipedia]