I would like to add more information to the @Neil Slater's answer.
Andrew sir has used a "generic" graph to show min loss function mean higher performance. That is not always the case, sometimes its over fitting. Let's no go into that realm of machine learning I am not that pro
The output of the function in maths is called
range and input is called
domain. We are using MSE in the linear regression because it is sensitive to the outliers and help in penalizing the parameters to get more accurate value that fits the training example (aka line of best fit).
In the MSE, the minimum loss would be $\hat y$ = y which means the difference is $0$, so does the mean $\mu$ would be zero. Therefore the range of function would be $[0, \infty)$. In case of MSE, the min value of the cost function would be $0$ no matter what.
Do not confuse the $0$ min value of the MSE with the min $0$ of gradient descent of the cost function. Remember, in the gradient descent there is no 2 in the power, it can be negative, despite being positive value of the MSE function.