Nothing happens during this time. They just dont want you to start being a burden on their healthcare system until you've been there for 3 months. Normally when you move within Canada, you are covered by the province you lived in previously for the first 3 months, after that your new province kicks in. Maybe they do this because too many people move somewhere, stay a month and change their minds and go back and it's too much paperwork on the healthcare. Maybe they don't really consider you to be living somewhere until you've been there 3 months, otherwise you are just a tourist to them. I really don't know.
Some provinces make exceptions for people who are moving from another country and cover them from the first day. If you are not moving to one of them, you have to get yourself private insurance if you want to be covered for the first 3 months. I actually don't consider this 3 months too bad. In my homeland and definitely some of the neighbouring countries as well, you have to live there for 6 months until you get into the health care system.
