If something happens punctually, it happens at the exact time that was arranged — the train at 9:00, the class at 10:00, the payment on the first of the month. It is the adverb of being on time, and it sounds a little more careful and formal than a plain 'on time'. Teachers, offices, and timetables like this word. Though actually, people rarely mean 'to the second'. In real life, arriving at 8:58 for a 9:00 meeting counts as punctually; arriving at 9:10 does not. The word is about not being late and not keeping others waiting, not about a stopwatch. You can use it for people (she arrived punctually) and also for things (the bus left punctually). It does not mean 'quickly' — a slow worker can still finish punctually if they finish when they said they would.

準時地