Machine Learning is mainly 3 kinds of algorithms - Supervised, Unsupervised and Reinforcement learning. In supervised learning, the training data set has certain input column and one of more output columns. Both the input and output columns ‘supervise’ the training of the model.
The way they ‘supervises’ is by determining the prediction error which is the difference between what the current state of the model outputs vs. what the actual output should be.
This way you try to improve the model in multiple iterations by minimizing the error, and the actual value of the output (and weights assigned to the inputs) ‘supervising’ the direction of the model in each iterations. If there were no output values (like in clustering, which is unsupervised learning) then you will never know how good your model is predicting and you will not be able to supervise it for better accuracy.
While the above approach is how most ML algorithms work, some ML algorithms are closed form in nature (meaning they have a ready made Math formula). Both simple and multi-variate regression are examples for these. If you do regression using the closed form formula you plug in the inputs and outputs at the same time into the equation and out comes the weights. This is still supervised learning as both inputs and outputs determine the final state of your model.