A VAE learns to compress data into a smooth probabilistic space and rebuild it, which lets you generate new samples by picking points in that space.
A GAN learns by competition and produces sharper output with unstable training. A VAE learns by reconstruction, trains reliably, and produces blurrier results.
A variational autoencoder learns to compress data into a compact space and rebuild it from there. The compressed space is probabilistic and smooth, which is what makes generating new samples possible.
An ordinary autoencoder learns fixed points, so the space between them is meaningless. A VAE encodes to a distribution instead, which forces the space to be continuous. Points near each other decode to similar things.
Think of it like this. Think of describing faces by a handful of dials rather than pixel by pixel. Because the dials vary smoothly, turning one slightly gives you a slightly different face rather than noise.