"Latent" means hidden: variables that are not directly observed but organize what is. In deep learning, the latent space is the space of a model's internal representations: each datum corresponds to a point (a vector), and the geometry of the space reflects similarities.
Why there is such a thing. Chollet (2021) explains it with the manifold hypothesis: natural data occupy a tiny, highly structured region of the space of possible inputs. Of all 28×28-pixel images, almost none look like a digit, and those that do form a continuous low-dimensional "manifold". A deep model learns to "uncrumple" that manifold, like smoothing out a ball of paper, and generalizes by interpolating along it; interpolating in latent space is not averaging pixels, since the average of two digits is not a digit (2021, sec. 5.1.2).
In generative models the latent space is the starting point. The encoder of a VAE maps each image to a distribution in that space and the decoder goes back from there to images (Kingma & Welling, 2014). In a GAN, the generator starts from random noise that means nothing at first; training makes its coordinates come to encode combinations of features (Buckner, 2024, pp. 207–209). This allows interpolation (rotating a face, changing its age) and arithmetic: "man with glasses" − "man" + "woman" yields images of women with glasses (Buckner, 2024, pp. 212–213). Latent diffusion works in the latent space of an autoencoder to save compute (Rombach et al., 2022), and in CLIP texts and images share a single space.
A philosophical angle. The idea recalls the conceptual spaces of Gärdenfors (2000), which Buckner (2024) uses to think of categories as regions of a similarity space (2024, pp. 114–115). But there is a difference: Gärdenfors's dimensions (hue, brightness) have names; those of a latent space do not, and finding names for them is the work of interpretability, not a given. That a direction "means" glasses is a hypothesis to be tested, not something the model declares.