Latent Dirichlet Allocation, LDA, is a generative model that allows sets of observations to be explained by unobserved groups that explain why some parts of the data are similar.
If observations are words collected into documents, it posits that each document is a mixture of a small number of topics and that each word's creation is attributable to one of the document's topics. LDA represents documents as mixtures of topics that spit out words with certain probabilities.
It should not be confused with Linear Discriminant Analysis, a supervised learning procedure for classifying observations into a set of categories.