Weighted versus arithmetic mean
In an arithmetic mean every number counts the same. In a weighted mean each carries its own weight — an end-of-topic test counts for more than a short quiz. That is why your reported average is almost never the plain average of your marks.
When the median says more than the mean
The mean is sensitive to outliers: a single very low mark can drag a whole term down. The median — the middle value once the list is sorted — ignores the extremes, so it often describes the typical mark better.
The mode — the most common value
The mode is the value that appears most often. In the set 4, 4, 5, 3 the mode is 4. If every value appears exactly once there is no mode at all, and the calculator says so explicitly.