Squashing data with a great many columns down to a handful while keeping most of what matters. Useful for plotting something on a page when it really has two hundred dimensions, for speeding up other models, and for stripping out noise. Something is always lost; the skill is in losing the right something.
Technical view
Principal component analysis finds orthogonal directions of maximum variance and projects onto the first few; it is linear, fast and reversible. Non-linear methods such as t-SNE and UMAP are used mainly for visualisation and preserve local neighbourhood structure at the expense of global distances, which means the gaps between clusters in such a plot should not be read as meaningful. Autoencoders learn a compressed representation through a bottleneck layer and are the neural equivalent. Embeddings are a close relative arrived at from the opposite direction.
Related
Part of AI Terminology Index, section: Classical Machine Learning.