Systems that produce new content rather than sorting or labelling existing things. Text, images, audio, video and code. The distinction matters because it changes what the technology is for: a classifier tells you which bucket something belongs in, whereas a generative system creates something that did not exist before.
Technical view
Different modalities use different approaches. Language models generate sequentially, one token at a time. Image models typically use diffusion, starting from random noise and iteratively removing it under the guidance of a text description. Generative systems introduce evaluation problems that classifiers do not have, since there is often no single correct output to measure against, which is why human preference judgements play such a large role.
Related
Part of AI Terminology Index, section: Extending and Applying Models.