In the tutorial, they normalize the data and say "The mean and standard deviation should only be computed using the training data"
What does this refer to? Why should you only use the training data?
When building any Machine Learning model, the only observable data you have is training data. Test data is supposed to be unobserved data, meaning that even though you might have it now, you need to act as if you didn't. When you apply normalisation, you first observe the data to get the parameters you need. As you are only supposed to be able to observe the training data, you can't use the test data to calculate those values. Doing so would be like cheating, as you are accomodating your parameters to new unobserved data (how can you observe unobserved data?).
Imagine you build a model today and you want to make predictions tomorrow. You can't use tomorrow data to build your model since you don't have it yet. You are not supposed to know tomorrow's mean and std, though your hope is that they will be similar enough. That is why when you normalose/standarise you get the parameters with the training data and then use them to transform both train and test data, so you can use them as inputs for your model.