What does ‘ten of six’ mean in regard to time?

In American English, using “of” when telling the time denotes the number minutes before the upcoming hour. Thus, “ten of six” would mean 5:50 p.m. As another example, “quarter of three” would be 2:45 p.m.

In the British, “to” is used instead of “of”. Thus, 5:50 p.m. would be “ten to six” and 2:45 p.m. would be “quarter to three”. Americans also use “to” when telling the time.)

To indicate the minutes following the hour, “after” or “past” is used. Thus, 6:10 p.m. would be expressed as “ten past six” or “ten after six”. I’m of the opinion that “past” is more commonly used in British strains, while “after” is mostly American.

While most people just say the numbers these days, e.g. “six-ten”, “five-fifty”, etc, “ten of–” is still quite popular, as well as “five of–“, though to a lesser degree. You probably would not hear “twenty of–” or “twenty-five of–” too often.