Like in Michael's example, it means 'exactly' on time.
For example, maybe you said to a friend that you would meet at 4:00 pm. It is 3:59 and your friend still hasn't arrived - usually you might expect them to arrive a bit earlier. Suddenly at 4:00 they show up. You might say to them "Right on time!", as they arrived exactly on the agreed time.
It can be a bit similar to "just in time" because if it is one minute later than the agreed time, this would be late.
Another example could be if you are going to catch a bus. The bus company asks you to arrive 10 minutes before departure. Someone arrives maybe one minute before the bus departs. As soon as they get on the bus, the bus leaves. They might say "Right on time!" as a kind of funny thing - they arrived exactly at the moment before the bus left, even though the actual time they were supposed to arrive was ten minutes beforehand (it may be seen as funny because though they say “right on time" they are actually not right on time - they have arrived ten minutes later than they were asked to). In this situation, it is very similar to "just in time" - they arrived 'just' before the bus departed.