Public school means different things in different countries.
The United States
Public school in the United States means a school funded by taxpayers where children get free education. However at least part of information learned at school is useless and/or forgotten immediately after the test with the information on it is finished. In the United States religious education and classroom prayer in public schools is unconstitutional. Kids may pray by themselves or form prayer clubs but can’t officially be forced to take part. Sex education is allowed but abstinence education sometimes takes the place of teaching about birth control. Naturally this adds to the teen pregnancy problem. More liberal school systems teach birth control. Some Americans think kids should get birth control advice and help with contraception, others think girls who have sex too early should be punished by having babies too early. 
Public school in Australia means basically the same thing as in the US, but parents have to pay for it, through school fees as well. These schools are also referred to as "Mainstream schools".
- Public school in the United Kingdom means a very select private school (which raises the question 'why are they called public schools?'). Traditionally British Public schools were boarding schools where parents from the elite would send their sons to get beaten by headmasters, housemasters and prefects. Today corporal punishment is illegal in British schools. Rich parents pay very high fees to get their children, (usually sons) a select education at public schools. Some British public schools accept girls especially 16 years old or over in the 6th form. A large number of private schools in Britain are same-sex, that is to say they usually produce young men who snigger (politely?) behind their hands whenever they see a pair of breasts on TV, and are still under the impression that girls have germs.
In the United Kingdom what America calls public schools are called "State schools" and the culture is different. For example children are forced to take part in religious worship unless their parents agree to them stopping.