ICAO allocate the first two characters of the ICAO code to the various worldwide regions and countries, but let them decide their own local coding of the last two characters, so there are a range of different approaches. Thus Britain got E for Europe and G for Great Britain, then chose to have the third character showing the area, last character for individual airport within that. Germany chose to do it a bit differently, assigned ED for Europe, Deutschland, then they chose D for major airports and last character meaningful, hence EDDF for Frankfurt and EDDH for Hamburg.
USA was always going to have a vast number, so they were just given one prefix letter, K, and allowed three to identify the individual airport. As 3-character airport codes were already in local use there they just stuck the K on the front to give the ICAO code, hence KMIA for Miami etc. When IATA codes came along they just used these existing 3-character codes.
Canada were ICAO region C, country Y, thus like most other countries they only had two remaining characters to play with. They tried to make the remainder a bit meaningful, thus CYVR for Vancouver or CYTO for Toronto. When IATA came along Canada and US were in the same area and the approach to chop off the first letter to make the IATA code was adopted for both countries, thus all Canadian IATA codes start with Y.
Canada is a big country so all the good codes got used up quickly. As new airports opened they had to make do with what was left. When Toronto Pearson was opened to replace Downsview they had to make do with YZ as a suffix, thus ICAO code CYYZ and IATA code YYZ. Similar elsewhere round the country.