For each element in the test set, we know its actual class (true class) and the class our classifier predicts (predicted class).
In a binary classification problem, we have only two classes: positive and negative. However, in a multiclass confusion matrix, we no longer have "positive" and "negative" classes, so it does not make sense to use those concepts here.
In a multiclass confusion matrix, the concept of "positive" and "negative" classes from binary classification is replaced with the individual classes of the problem.
Instead, in a multiclass confusion matrix, we count the class each element is predicted to belong to (columns) depending on its true class (rows). This way, in the diagonal, you find the elements that were correctly classified (predicted class matches true class) while in the non-diagonal elements, you see the number of misclassified elements. The higher the counts in the diagonal, the better your classifier is. If we look at the columns, we can see, for each predicted class, what the actual true classes were. If we look at the rows, we can see, for each true class, what the predicted classes were.
In the matrix, we can quickly see if we are consistently misclassifying one class for another one. For instance, in your matrix, we can see that class 0 is sometimes (5 times) misclassified as class 3. If the problem were worse, we might decide to try to get more data from these classes to train a better classifier.