For supervised learning you use labeled training set to train whatever model you have. You can then use the model to predict labels for an unlabeled set.
If you happen to have labels for the test set too, you can compare the predicted values to the test set labels. This way you can assess the prediction error (i.e. test the model, hence the name - test set)
If you are however only interested in the prediction, you definitely don't need the labels.