Repeated training and testing in Weka?
In general the advantage of repeated training/testing is to measure to what extent the performance is due to chance. The most common source of chance comes from which instances are selected as training/testing data. One can use k-fold cross-validation in order to mitigate the effect of chance in this case. Weka performs 10-fold CV by default, as far as I remember, but this is not compatible with providing a specific training/test set.



[edit based on OP's comments]

In the video mentioned by OP, the author loads a dataset and sets the "percentage split" at 90%. This means that the full dataset will be split between training and test set by Weka itself. Weka randomly selects which instances are used for training, this is why chance is involved in the process and this is why the author proceeds to repeat the experiment with different values for the random seed: every time Weka will selects a different subset of instances as training set, resulting in a different accuracy. In other words, the purpose of repeating the experiment is to change how the dataset is split between training and test set. In this case (J48 with default options) there would be no point repeating the experiment with a fixed training set, because there's no chance involved in the process so there's no variation in the result.

It's worth noticing that this lesson by the author of the video seems to be used as an introduction to the more general concept of k-fold cross-validation, presented a couple of lessons later in the course.