These express the number of times something happens, i.e. the number of occurrences. While once and twice are commonly used, and therefore relevant to EFL pedagogy, thrice is seldom used.
They can be used as the denominator to make frequency adverbials, e.g. twice a week or once per day.
Numbers higher than 3 cannot be expressed with single words. Rather, we must use equivalent phrases; numeral adverbial phrases, such as four times, five times, etc. The number 0 is also difficult to express; we tend to use never, though that technically is a temporal frequency adverb, any fraction with 0 as numerator is equal to 0.
Once can mean one time, but can also mean “when” or “as soon as”.
These are a type of frequency adverb that refer to absolute frequency. This can perhaps be best illustrated by considering the wh- phrase needed; for absolute frequency it is how many times, but for temporal frequency it is how often.