When a model learns its training examples so closely that it fails on anything new. It is the equivalent of memorising past exam papers instead of understanding the subject: flawless on questions you have seen, lost on anything else. The opposite failure, underfitting, means the model is too simple to capture the real pattern at all.
Technical view
This is the bias-variance trade-off. It is detected by watching training loss continue to fall while validation loss starts rising. Standard countermeasures include regularisation, dropout, early stopping, and augmenting or increasing training data. A related and serious practical problem is data leakage, where information from the test set contaminates training, producing results that look excellent and collapse in the real world.
Related
Part of AI Terminology Index, section: How the Machinery Works.