Topfreedom is a concept of rights. Topfreedom applies to women. It means the freedom to go topless (without wearing any clothing above the waist) in a public place.
There are many organizations which advocate topfreedom. Topfree Equal Rights Association (TERA) is one such organization. Go Topless Day is a special day in August. In this day, women are told to go topless in public.
In the United States, each state has its own laws. The New York State Supreme Court said that women can go topless in public. Later, the police arrested a woman (in 2005) in New York City for walking along a street without wearing a shirt. She sued (started a court case against) the city for violating the New York State Supreme Court rule that women can go topless in public. The city finally paid her $29,000 because she was right and the police were wrong.
In three provinces in Canada (Ontario, Manitoba and British Columbia) women can be topless in public. However there are sometimes city laws saying women cannot be topless in city parks. Law professors say women probably can be topless in public in the other provinces, but nobody knows for sure. The question has not been decided by the Supreme (national) Court of Canada.
Sometimes women who swim "topless" in the United States use pasties to cover their nipples. It can be a protest against laws telling them to cover their breasts.