In supervised learning the data are pairs (input, expected answer): photos labeled "cat" or "dog," emails marked spam or not, houses with their prices. The answer is called the target, label, or annotation (Chollet, 2021, sec. 7.4), and the model learns a function that reproduces it for inputs it has not seen. Depending on the kind of answer, the task is classification (categories) or regression (numbers). Witten et al. (2017) explain the name: the algorithm operates under supervision because it is given the actual outcome for each training example (2017, p. 45).
The origins are behaviorist. M. Mitchell (2019) recounts that Rosenblatt, inspired by Skinner's conditioning, wanted the Perceptron to be rewarded when it was right and punished when it erred; that form of conditioning is what is now called supervised learning, with a supervision signal telling the system how far its output was from the correct one (2019, ch. 1).
Labels do not fall from the sky: someone produces them, often workers on microtask platforms such as Mechanical Turk, who labeled ImageNet (M. Mitchell, 2019, ch. 5) (see data annotation). That is why nearly everyone in the field agrees that supervised learning is not, on its own, a viable path to general AI: you cannot label the whole world, and there is always a "long tail" of rare situations with no examples (M. Mitchell, 2019, ch. 6).
For the philosopher of language, learning from labeled examples resembles ostensive teaching and inherits its problem: an ostensive definition can be variously interpreted (Wittgenstein, 1953/2009, §28). A finite set of pairs fixes, at most, part of a concept's extension; many different functions fit the same labels, and which one the model picks depends on its inductive bias.