An autoencoder that learns a distribution rather than a single point for each input, which makes the compressed space smooth enough to generate from. Pick a point at random in that space and decode it and you get something plausible, which a plain autoencoder cannot reliably do.
Technical view
Encodes to parameters of a distribution and optimises the evidence lower bound: reconstruction quality minus the Kullback-Leibler divergence from a prior, usually a standard normal. The reparameterisation trick makes sampling differentiable. Outputs tend to be blurry compared to diffusion or adversarial models, but the learned latent space is well structured, and VAEs remain a standard component compressing images before latent diffusion operates on them.
Related
Part of AI Terminology Index, section: How the Machinery Works.