Generative models are models that learn the joint probability distribution of the input and output variables. They learn the probability of a certain output given a certain input. For example, a generative model could be used to learn the probability of a person having a certain disease given their symptoms.
Discriminative models are models that learn the conditional probability of an output given an input. They learn the probability of an output given a certain input, without learning the joint probability distribution of the input and output variables. For example, a discriminative model could be used to learn the probability of a person being diagnosed with a certain disease given their symptoms.